1 00:00:00,000 --> 00:00:02,520 The following content is provided under a Creative 2 00:00:02,520 --> 00:00:03,970 Commons license. 3 00:00:03,970 --> 00:00:06,360 Your support will help MIT OpenCourseWare 4 00:00:06,360 --> 00:00:10,660 continue to offer high-quality educational resources for free. 5 00:00:10,660 --> 00:00:13,350 To make a donation or view additional materials 6 00:00:13,350 --> 00:00:17,190 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,190 --> 00:00:18,332 at ocw.mit.edu. 8 00:00:27,342 --> 00:00:29,050 JEFFREY GROSSMAN: That is the point here. 9 00:00:29,050 --> 00:00:34,300 This is not a heavy math derivation kind of thing. 10 00:00:34,300 --> 00:00:36,610 This is not-- we are not going to go 11 00:00:36,610 --> 00:00:40,070 into great mathematical detail in quantum mechanics. 12 00:00:40,070 --> 00:00:41,560 Now, we will show some equations, 13 00:00:41,560 --> 00:00:43,060 we'll work with equations, because I 14 00:00:43,060 --> 00:00:44,352 want you to know what they are. 15 00:00:44,352 --> 00:00:46,240 You got to know what's under the hood. 16 00:00:46,240 --> 00:00:48,910 But we're not going to go into sort of gory detail 17 00:00:48,910 --> 00:00:51,580 in solving complex quantum problems on paper. 18 00:00:51,580 --> 00:00:55,730 That's where the tools help lift you away from that. 19 00:00:55,730 --> 00:00:58,480 And it also is kind of the flavor of this class, which 20 00:00:58,480 --> 00:01:01,030 is that this is about practice. 21 00:01:01,030 --> 00:01:06,970 This is about learning the basic concepts, 22 00:01:06,970 --> 00:01:09,610 and then applying them to real problems and materials. 23 00:01:09,610 --> 00:01:13,600 And my enjoyment is in energy, so the problems 24 00:01:13,600 --> 00:01:16,255 we'll do in this part are going to be energy-related problems. 25 00:01:19,600 --> 00:01:23,182 How many of you have had quantum mechanics? 26 00:01:23,182 --> 00:01:24,640 I wouldn't have expected that many. 27 00:01:24,640 --> 00:01:29,980 How many of you have never seen quantum mechanics in any form? 28 00:01:29,980 --> 00:01:31,480 Raise your hands, because it's good. 29 00:01:31,480 --> 00:01:32,350 It's good. 30 00:01:32,350 --> 00:01:36,640 We're going to start-- we're going to do quantum mechanics-- 31 00:01:36,640 --> 00:01:38,920 we're going to do a couple lectures here-- oh, this 32 00:01:38,920 --> 00:01:40,003 is what we're going to do. 33 00:01:43,070 --> 00:01:45,438 That's our outline for the class, for the second half. 34 00:01:45,438 --> 00:01:47,230 And you can see that what we're going to do 35 00:01:47,230 --> 00:01:49,510 is we're going to kind of gently learn 36 00:01:49,510 --> 00:01:51,250 the key aspects of quantum mechanics 37 00:01:51,250 --> 00:01:53,950 that I'd like you to know for the modeling 38 00:01:53,950 --> 00:01:56,320 that we're going to do of materials. 39 00:01:56,320 --> 00:01:58,600 And then we're going to actually apply it. 40 00:01:58,600 --> 00:02:01,012 We're going to stop right here in the derivations, 41 00:02:01,012 --> 00:02:02,470 in the theory, and then we're going 42 00:02:02,470 --> 00:02:04,428 to start applying that to real energy problems. 43 00:02:04,428 --> 00:02:06,520 So then we're going to do two lectures 44 00:02:06,520 --> 00:02:09,940 on how to apply what we just learned to two different energy 45 00:02:09,940 --> 00:02:11,410 topics. 46 00:02:11,410 --> 00:02:13,660 One, solar thermal fuels. 47 00:02:13,660 --> 00:02:15,830 Very cool and exciting material. 48 00:02:15,830 --> 00:02:17,800 And another, hydrogen storage. 49 00:02:17,800 --> 00:02:20,200 Also very cool and exciting. 50 00:02:20,200 --> 00:02:22,930 Then we're going to turn to how you go from modeling atoms 51 00:02:22,930 --> 00:02:25,270 to modeling solids with quantum mechanics, 52 00:02:25,270 --> 00:02:27,520 where different things happen. 53 00:02:27,520 --> 00:02:30,340 How many of you have heard of a band structure? 54 00:02:30,340 --> 00:02:31,570 Yeah. 55 00:02:31,570 --> 00:02:35,190 Now, how many of you can tell me, from the band structure, 56 00:02:35,190 --> 00:02:38,700 why silicon solar cells are too expensive? 57 00:02:38,700 --> 00:02:42,090 Now, you will be able to tell me that right here. 58 00:02:42,090 --> 00:02:43,800 We're going to know. 59 00:02:43,800 --> 00:02:45,540 And that's a really exciting thing, 60 00:02:45,540 --> 00:02:47,820 because it's all in the band structure. 61 00:02:47,820 --> 00:02:50,110 That answer is all in the band structure. 62 00:02:50,110 --> 00:02:54,330 So many properties of materials come out of these basic quantum 63 00:02:54,330 --> 00:02:58,560 mechanical property maps that you get. 64 00:02:58,560 --> 00:03:00,490 So that's what we're going to do here. 65 00:03:00,490 --> 00:03:03,150 And then we'll go more general and do applications 66 00:03:03,150 --> 00:03:06,390 in nanotechnology and more broadly. 67 00:03:06,390 --> 00:03:09,300 How many of you have heard of quantum confinement? 68 00:03:09,300 --> 00:03:10,620 That's down here. 69 00:03:10,620 --> 00:03:12,180 Do you know what it is? 70 00:03:12,180 --> 00:03:13,460 Somebody tell me what it is. 71 00:03:13,460 --> 00:03:14,610 Yeah. 72 00:03:14,610 --> 00:03:15,193 AUDIENCE: So-- 73 00:03:15,193 --> 00:03:16,318 JEFFREY GROSSMAN: Oh, yeah. 74 00:03:16,318 --> 00:03:17,387 AUDIENCE: What is it? 75 00:03:17,387 --> 00:03:19,220 JEFFREY GROSSMAN: Yeah, yeah, let's hear it. 76 00:03:19,220 --> 00:03:20,010 AUDIENCE: So what is it? 77 00:03:20,010 --> 00:03:21,560 So you have the [? key, ?] [? and that ?] [? holds ?] 78 00:03:21,560 --> 00:03:24,210 electrons, stuff like that, and they both [INAUDIBLE] take 79 00:03:24,210 --> 00:03:29,290 a small section, it's so small that it emits different 80 00:03:29,290 --> 00:03:29,790 colors-- 81 00:03:29,790 --> 00:03:30,290 I mean, I don't know. 82 00:03:30,290 --> 00:03:31,170 JEFFREY GROSSMAN: Yeah. 83 00:03:31,170 --> 00:03:32,045 That's exactly right. 84 00:03:32,045 --> 00:03:33,810 Now, but why? 85 00:03:33,810 --> 00:03:36,330 You have electrons and holes, which are just positive 86 00:03:36,330 --> 00:03:40,010 and negative charges, right? 87 00:03:40,010 --> 00:03:41,150 You talked about that. 88 00:03:41,150 --> 00:03:44,290 And then you make it small, and it emits a different color 89 00:03:44,290 --> 00:03:45,250 light. 90 00:03:45,250 --> 00:03:46,708 What emits a different color light? 91 00:03:46,708 --> 00:03:47,625 AUDIENCE: Quantum dot. 92 00:03:47,625 --> 00:03:49,560 JEFFREY GROSSMAN: Quantum dot, for example. 93 00:03:49,560 --> 00:03:51,460 Now, why? 94 00:03:51,460 --> 00:03:52,630 Can anybody tell me why? 95 00:03:52,630 --> 00:03:55,240 AUDIENCE: The [? sides ?] all emit from a certain wavelength? 96 00:03:55,240 --> 00:03:58,150 JEFFREY GROSSMAN: Why? 97 00:03:58,150 --> 00:04:03,310 Changes the fundamental gap of the material, but why? 98 00:04:03,310 --> 00:04:05,080 It's something called quantum confinement. 99 00:04:05,080 --> 00:04:08,710 Actually, it's nothing more than what those two words say. 100 00:04:08,710 --> 00:04:13,220 Quantum confinement is the squeezing of quantum things. 101 00:04:13,220 --> 00:04:15,100 And in this case, our quantum things 102 00:04:15,100 --> 00:04:18,880 are positive and negative charges. 103 00:04:18,880 --> 00:04:19,899 Right? 104 00:04:19,899 --> 00:04:23,448 And it turns out, when you make an expectation, 105 00:04:23,448 --> 00:04:25,240 the positive and negative charge like to be 106 00:04:25,240 --> 00:04:26,630 kind of close to each other. 107 00:04:26,630 --> 00:04:28,840 They don't like to go away, necessarily. 108 00:04:28,840 --> 00:04:31,510 Sometimes they like to stay close. 109 00:04:31,510 --> 00:04:33,610 But they don't like to get too close. 110 00:04:33,610 --> 00:04:36,010 So if you make the material smaller than the closeness 111 00:04:36,010 --> 00:04:37,720 they like to get, then they're squeezed. 112 00:04:37,720 --> 00:04:38,590 They're confined. 113 00:04:38,590 --> 00:04:41,430 And when you confine quantum things, 114 00:04:41,430 --> 00:04:43,560 you get interesting effects. 115 00:04:43,560 --> 00:04:47,370 That's why I can take something that, say, ordinarily looks 116 00:04:47,370 --> 00:04:49,470 like this, and take a small piece of it, 117 00:04:49,470 --> 00:04:51,600 and all of a sudden, it turns blue. 118 00:04:51,600 --> 00:04:53,250 Like, how cool is that? 119 00:04:53,250 --> 00:04:55,650 You changed the color just by changing the size. 120 00:04:55,650 --> 00:04:57,150 That's quantum confinement. 121 00:04:57,150 --> 00:04:59,400 That's something that has everything 122 00:04:59,400 --> 00:05:01,590 to do with quantum mechanics. 123 00:05:01,590 --> 00:05:02,260 Right? 124 00:05:02,260 --> 00:05:05,370 Electrons and holes, positive and negative charges. 125 00:05:05,370 --> 00:05:08,220 You're not going to get that-- 126 00:05:08,220 --> 00:05:09,945 you're not getting that over here. 127 00:05:09,945 --> 00:05:11,220 Mm-mm. 128 00:05:11,220 --> 00:05:12,608 That's part one. 129 00:05:12,608 --> 00:05:14,400 Now we're going to go to quantum mechanics. 130 00:05:14,400 --> 00:05:16,650 Because you can't simulate electrons and holes 131 00:05:16,650 --> 00:05:19,020 in part one, but now you can. 132 00:05:19,020 --> 00:05:20,430 Well, you will be able to. 133 00:05:20,430 --> 00:05:21,930 And we're going to actually-- you're 134 00:05:21,930 --> 00:05:24,900 going to be able to tell me what color a quantum dot could 135 00:05:24,900 --> 00:05:28,620 be just by solving these equations on a computer. 136 00:05:28,620 --> 00:05:31,500 Because now we're going to capture quantum mechanics 137 00:05:31,500 --> 00:05:33,450 and apply it to things like nanotechnology. 138 00:05:33,450 --> 00:05:35,550 OK, so that's just kind of a flavor 139 00:05:35,550 --> 00:05:37,610 of where we're going to go. 140 00:05:37,610 --> 00:05:38,710 Any questions? 141 00:05:42,189 --> 00:05:42,690 Mm-hmm. 142 00:05:45,600 --> 00:05:46,973 It's a quantum world. 143 00:05:46,973 --> 00:05:48,390 That's where we're going to start. 144 00:05:48,390 --> 00:05:51,540 And the reason I put this is because you can do Shakespeare 145 00:05:51,540 --> 00:05:52,267 very quickly. 146 00:05:52,267 --> 00:05:54,600 There are people who have been doing it for a long time. 147 00:05:54,600 --> 00:05:57,060 "Reducing expectations for over 20 years." 148 00:05:57,060 --> 00:05:59,203 I just like that quote. 149 00:05:59,203 --> 00:06:01,620 There is something called the Reduced Shakespeare Company. 150 00:06:01,620 --> 00:06:03,495 And that's what I'm going to try to do today. 151 00:06:03,495 --> 00:06:06,510 We're going to go through the basics of quantum mechanics 152 00:06:06,510 --> 00:06:08,790 in one lecture that's not really meant 153 00:06:08,790 --> 00:06:11,130 to teach you too much about quantum mechanics, 154 00:06:11,130 --> 00:06:12,450 or go too much into depth. 155 00:06:12,450 --> 00:06:15,990 Again, I want to go through some of the key aspects, 156 00:06:15,990 --> 00:06:18,030 but really to get a sense for it, 157 00:06:18,030 --> 00:06:20,940 not to go into great mathematical depth. 158 00:06:20,940 --> 00:06:23,290 That's what you take a quantum course for. 159 00:06:23,290 --> 00:06:24,390 OK? 160 00:06:24,390 --> 00:06:26,100 But I need you to understand some 161 00:06:26,100 --> 00:06:28,230 of the key aspects of quantum before we embark 162 00:06:28,230 --> 00:06:32,300 on modeling quantum mechanics. 163 00:06:32,300 --> 00:06:37,320 And so I want to start with why, and why did we 164 00:06:37,320 --> 00:06:38,940 even need this theory? 165 00:06:38,940 --> 00:06:41,260 And so we'll talk a little bit about that. 166 00:06:41,260 --> 00:06:43,710 And then we'll talk about some of the key aspects, which 167 00:06:43,710 --> 00:06:46,320 is this wave-particle duality. 168 00:06:46,320 --> 00:06:49,828 And then this is it right here. 169 00:06:49,828 --> 00:06:51,370 That's the equation we're going to be 170 00:06:51,370 --> 00:06:54,460 solving for all of part two. 171 00:06:54,460 --> 00:06:55,960 The Schrodinger equation. 172 00:06:55,960 --> 00:06:58,270 Has anybody seen the Schrodinger equation? 173 00:06:58,270 --> 00:06:59,290 Yeah, a little bit. 174 00:06:59,290 --> 00:07:05,215 Have any of you solved it for [? A? ?] I saw a so-so. 175 00:07:05,215 --> 00:07:08,007 A little kind of like you sort of solved it? 176 00:07:08,007 --> 00:07:08,840 What happened there? 177 00:07:08,840 --> 00:07:10,595 AUDIENCE: I solved it, but probably incorrectly. 178 00:07:10,595 --> 00:07:12,137 JEFFREY GROSSMAN: OK, I'll take that. 179 00:07:12,137 --> 00:07:12,655 That's good. 180 00:07:12,655 --> 00:07:14,780 And what else-- what other problems have you solved 181 00:07:14,780 --> 00:07:15,680 with the Schrodinger equation? 182 00:07:15,680 --> 00:07:15,900 Yeah. 183 00:07:15,900 --> 00:07:16,900 AUDIENCE: Hydrogen atom? 184 00:07:16,900 --> 00:07:18,500 JEFFREY GROSSMAN: Hydrogen atom, OK. 185 00:07:18,500 --> 00:07:20,897 That's where we'll end today. 186 00:07:20,897 --> 00:07:23,480 But still listen, because it's going to be really interesting. 187 00:07:23,480 --> 00:07:26,100 Any other-- who else has solved the Schrodinger equation? 188 00:07:26,100 --> 00:07:26,600 Yeah. 189 00:07:26,600 --> 00:07:27,767 AUDIENCE: Particle in a box. 190 00:07:27,767 --> 00:07:29,354 JEFFREY GROSSMAN: Particle in the box. 191 00:07:29,354 --> 00:07:30,562 AUDIENCE: Periodic potential? 192 00:07:30,562 --> 00:07:33,600 JEFFREY GROSSMAN: Periodic potential. 193 00:07:33,600 --> 00:07:34,110 Any others? 194 00:07:34,110 --> 00:07:34,350 Yeah. 195 00:07:34,350 --> 00:07:35,517 AUDIENCE: Quantum tunneling. 196 00:07:35,517 --> 00:07:37,770 JEFFREY GROSSMAN: Quantum tunneling, cool. 197 00:07:37,770 --> 00:07:38,770 Anyone else solve it? 198 00:07:38,770 --> 00:07:40,602 AUDIENCE: [INAUDIBLE] 199 00:07:40,602 --> 00:07:42,060 JEFFREY GROSSMAN: That's what we're 200 00:07:42,060 --> 00:07:43,428 going to do at the very end. 201 00:07:43,428 --> 00:07:44,470 That's the hydrogen atom. 202 00:07:44,470 --> 00:07:46,702 It's a harmonic potential. 203 00:07:46,702 --> 00:07:47,910 Somebody said something else? 204 00:07:49,918 --> 00:07:51,710 That's not quite a harmonic potential, but. 205 00:07:51,710 --> 00:07:52,895 AUDIENCE: Cat in the box. 206 00:07:52,895 --> 00:07:54,770 JEFFREY GROSSMAN: Any other-- cat in the box! 207 00:07:54,770 --> 00:07:58,250 I've got a cat in the box today for you! 208 00:07:58,250 --> 00:07:59,330 I put a cat in a box. 209 00:08:02,565 --> 00:08:04,940 The thing is, what's interesting about all those examples 210 00:08:04,940 --> 00:08:07,072 you all just said? 211 00:08:07,072 --> 00:08:08,530 AUDIENCE: They're all [INAUDIBLE].. 212 00:08:08,530 --> 00:08:09,488 JEFFREY GROSSMAN: Yeah. 213 00:08:09,488 --> 00:08:10,708 They're all kind of what? 214 00:08:10,708 --> 00:08:11,146 AUDIENCE: Simple. 215 00:08:11,146 --> 00:08:12,271 AUDIENCE: Exactly solvable. 216 00:08:12,271 --> 00:08:14,200 JEFFREY GROSSMAN: Exactly solvable and simple, 217 00:08:14,200 --> 00:08:15,820 and therefore? 218 00:08:15,820 --> 00:08:17,422 To someone in course three? 219 00:08:17,422 --> 00:08:18,130 AUDIENCE: Boring. 220 00:08:18,130 --> 00:08:19,250 JEFFREY GROSSMAN: Eh. 221 00:08:19,250 --> 00:08:20,760 Right? 222 00:08:20,760 --> 00:08:24,780 That's where we have changed so much 223 00:08:24,780 --> 00:08:28,820 in what we can do because of computation. 224 00:08:28,820 --> 00:08:34,340 So now, because of the approximations 225 00:08:34,340 --> 00:08:37,179 that you're going to learn in the next couple of lectures, 226 00:08:37,179 --> 00:08:40,330 and the speed of computers, we can actually 227 00:08:40,330 --> 00:08:44,110 solve the Schrodinger equation for realistic materials. 228 00:08:44,110 --> 00:08:45,970 That's why we can have this class. 229 00:08:45,970 --> 00:08:47,980 We would not be having this class-- 230 00:08:47,980 --> 00:08:48,670 no. 231 00:08:48,670 --> 00:08:51,610 We wouldn't be having part two of this class back 232 00:08:51,610 --> 00:08:53,950 in the 1970s, 1980s. 233 00:08:53,950 --> 00:08:54,940 Oh, that reminds me. 234 00:08:54,940 --> 00:08:56,950 You should go to Berni Alder. 235 00:08:56,950 --> 00:08:59,350 Are all of you aware of Berni Alder's talk? 236 00:08:59,350 --> 00:09:03,430 He is really one of the key foundations 237 00:09:03,430 --> 00:09:07,330 of computational science in this country and in the world. 238 00:09:07,330 --> 00:09:10,690 And he contributed to some of the very first 239 00:09:10,690 --> 00:09:13,120 molecular dynamic simulations ever done. 240 00:09:13,120 --> 00:09:15,440 And really helped-- and that was in the 1950s. 241 00:09:15,440 --> 00:09:16,870 So he's going to be a speaker. 242 00:09:16,870 --> 00:09:17,858 Who can tell me when? 243 00:09:17,858 --> 00:09:18,650 AUDIENCE: Tomorrow. 244 00:09:18,650 --> 00:09:20,108 JEFFREY GROSSMAN: Tomorrow at 4:00. 245 00:09:20,108 --> 00:09:22,440 Where? 246 00:09:22,440 --> 00:09:27,323 Somewhere on this campus, Berni Alder will be speaking at 4:00. 247 00:09:27,323 --> 00:09:28,740 Please find him and go if you can. 248 00:09:28,740 --> 00:09:34,367 He just really made some really important key contributions 249 00:09:34,367 --> 00:09:35,950 to this field and helped to launch it. 250 00:09:35,950 --> 00:09:38,010 It gave credibility. 251 00:09:38,010 --> 00:09:41,940 He saw-- in molecular dynamics simulations in the 1950s, 252 00:09:41,940 --> 00:09:45,780 he could see really interesting phenomena-- phase transitions 253 00:09:45,780 --> 00:09:46,800 happening in materials. 254 00:09:46,800 --> 00:09:49,560 Really helped to launch the field of computation 255 00:09:49,560 --> 00:09:51,570 in materials. 256 00:09:51,570 --> 00:09:53,160 OK, so let's go. 257 00:09:53,160 --> 00:09:56,040 So here, you've seen this picture in the first part. 258 00:09:56,040 --> 00:09:59,220 And you've also seen this. 259 00:09:59,220 --> 00:10:00,990 And, see, this is what? 260 00:10:00,990 --> 00:10:02,460 In part one, this is what? 261 00:10:05,196 --> 00:10:06,482 AUDIENCE: [INAUDIBLE] 262 00:10:06,482 --> 00:10:07,440 JEFFREY GROSSMAN: Yeah. 263 00:10:07,440 --> 00:10:09,720 Force field, Lennard-Jones. 264 00:10:09,720 --> 00:10:12,810 And where do you get that? 265 00:10:12,810 --> 00:10:14,340 Because you need it, right? 266 00:10:14,340 --> 00:10:17,620 Can you do part one without that? 267 00:10:17,620 --> 00:10:19,140 Now, so where do you get it? 268 00:10:19,140 --> 00:10:20,630 AUDIENCE: Quantum [INAUDIBLE]. 269 00:10:20,630 --> 00:10:22,370 JEFFREY GROSSMAN: Well, you could. 270 00:10:22,370 --> 00:10:24,289 Or you could get it from where? 271 00:10:24,289 --> 00:10:25,164 AUDIENCE: [INAUDIBLE] 272 00:10:25,164 --> 00:10:26,890 JEFFREY GROSSMAN: Experiment. 273 00:10:26,890 --> 00:10:29,770 But see, if I'm making new materials that have never 274 00:10:29,770 --> 00:10:33,713 been made, or if I'm making materials where interactions 275 00:10:33,713 --> 00:10:36,130 are happening that I can't really measure, because they're 276 00:10:36,130 --> 00:10:39,130 really hard to measure, then where could you get something 277 00:10:39,130 --> 00:10:41,500 like this? 278 00:10:41,500 --> 00:10:43,240 You can't do the experiment. 279 00:10:43,240 --> 00:10:46,640 That's where we can go all the way down to here. 280 00:10:46,640 --> 00:10:49,030 And that's another place where this whole realm 281 00:10:49,030 --> 00:10:51,680 of quantum modeling is going to be important. 282 00:10:51,680 --> 00:10:54,940 So that's where we are, the bottom of the barrel. 283 00:10:54,940 --> 00:10:57,190 But not any less important. 284 00:11:00,560 --> 00:11:04,430 This is just-- this has nothing to do with quantum mechanics 285 00:11:04,430 --> 00:11:08,190 at all, but I thought it was pretty cool. 286 00:11:08,190 --> 00:11:09,260 Right? 287 00:11:09,260 --> 00:11:11,360 This is just a guy who has this-- 288 00:11:11,360 --> 00:11:14,500 he's got a camera pointing that way, 289 00:11:14,500 --> 00:11:16,510 and then he's got a little projector and a very 290 00:11:16,510 --> 00:11:18,730 specialized material here, and he's 291 00:11:18,730 --> 00:11:21,670 projecting the image onto his jacket, 292 00:11:21,670 --> 00:11:23,470 and so it looks like he's transparent. 293 00:11:23,470 --> 00:11:28,220 But the point being that I thought it was a cool idea, 294 00:11:28,220 --> 00:11:28,720 I guess. 295 00:11:30,850 --> 00:11:32,480 Sort of interesting. 296 00:11:32,480 --> 00:11:35,080 So you can see, the car's sort of there, 297 00:11:35,080 --> 00:11:37,010 but I don't think the car's really there. 298 00:11:37,010 --> 00:11:39,150 Anyway, he needs to focus it. 299 00:11:39,150 --> 00:11:42,400 But weird things happen in quantum mechanics. 300 00:11:42,400 --> 00:11:43,870 Really, really weird things. 301 00:11:43,870 --> 00:11:46,120 And it is a very quantum world. 302 00:11:46,120 --> 00:11:50,230 If we understand those basic particles like electrons, 303 00:11:50,230 --> 00:11:53,910 then we can almost understand everything. 304 00:11:53,910 --> 00:11:55,830 Almost everything. 305 00:11:55,830 --> 00:11:57,600 Seriously. 306 00:11:57,600 --> 00:12:00,127 OK? 307 00:12:00,127 --> 00:12:01,710 So if you want to know the properties, 308 00:12:01,710 --> 00:12:04,320 like mechanical properties, and you 309 00:12:04,320 --> 00:12:07,230 have a good potential of this piece of iron, 310 00:12:07,230 --> 00:12:10,230 for this piece of iron, you can do classical mechanics. 311 00:12:10,230 --> 00:12:12,690 But if you want to understand the mechanical properties, 312 00:12:12,690 --> 00:12:14,000 and you don't have a good potential, 313 00:12:14,000 --> 00:12:15,450 well, you may need quantum mechanics. 314 00:12:15,450 --> 00:12:17,117 And certainly, if you want to understand 315 00:12:17,117 --> 00:12:21,850 the electrical properties, or the optical properties, 316 00:12:21,850 --> 00:12:25,570 can you do that with classical potentials? 317 00:12:25,570 --> 00:12:26,650 Tell me why. 318 00:12:26,650 --> 00:12:28,750 Why I can't get electrical properties 319 00:12:28,750 --> 00:12:32,670 with classical potentials? 320 00:12:32,670 --> 00:12:33,360 Yeah. 321 00:12:33,360 --> 00:12:35,880 AUDIENCE: Because you're modeling the entire atoms. 322 00:12:35,880 --> 00:12:37,920 You're just basically considering the nucleus 323 00:12:37,920 --> 00:12:39,360 and not really talking about the electrons. 324 00:12:39,360 --> 00:12:40,443 JEFFREY GROSSMAN: Exactly. 325 00:12:40,443 --> 00:12:43,262 And what do I need for electrical properties? 326 00:12:43,262 --> 00:12:45,990 You got to know about the electrons. 327 00:12:45,990 --> 00:12:47,560 Band structures! 328 00:12:47,560 --> 00:12:49,140 Band structures will tell us about 329 00:12:49,140 --> 00:12:51,630 the electrical properties. 330 00:12:51,630 --> 00:12:53,280 You will learn to see-- 331 00:12:53,280 --> 00:12:54,870 it's like The Matrix. 332 00:12:54,870 --> 00:12:58,140 You will learn to read band structures as whole cities 333 00:12:58,140 --> 00:13:00,480 to explore that tell you all about things 334 00:13:00,480 --> 00:13:02,020 like this, and this. 335 00:13:04,590 --> 00:13:06,480 It's really powerful. 336 00:13:06,480 --> 00:13:08,250 And it tells you-- and so all we need 337 00:13:08,250 --> 00:13:10,680 to do is go down one more scale, because this 338 00:13:10,680 --> 00:13:14,310 is where you've been, and this is where we're going. 339 00:13:14,310 --> 00:13:15,030 We're going here. 340 00:13:17,910 --> 00:13:21,190 Do electrons actually orbit? 341 00:13:21,190 --> 00:13:23,090 AUDIENCE: No. 342 00:13:23,090 --> 00:13:24,656 JEFFREY GROSSMAN: What do they do? 343 00:13:24,656 --> 00:13:26,450 AUDIENCE: Go around [INAUDIBLE]? 344 00:13:26,450 --> 00:13:27,840 JEFFREY GROSSMAN: They go around? 345 00:13:27,840 --> 00:13:29,090 AUDIENCE: No, they fly around. 346 00:13:29,090 --> 00:13:30,507 JEFFREY GROSSMAN: They fly around? 347 00:13:30,507 --> 00:13:31,180 Sounds better. 348 00:13:31,180 --> 00:13:31,680 What? 349 00:13:31,680 --> 00:13:32,670 AUDIENCE: They have their orbitals 350 00:13:32,670 --> 00:13:34,410 that they can-- that there's a possibility that they'll 351 00:13:34,410 --> 00:13:35,065 [? be at. ?] 352 00:13:35,065 --> 00:13:36,260 JEFFREY GROSSMAN: Yeah. 353 00:13:36,260 --> 00:13:36,980 Oh, yeah. 354 00:13:36,980 --> 00:13:38,830 That's where we're going. 355 00:13:38,830 --> 00:13:41,870 Why do we call them orbitals? 356 00:13:41,870 --> 00:13:43,370 Why do we call them orbitals? 357 00:13:43,370 --> 00:13:44,120 We'll get to that. 358 00:13:46,630 --> 00:13:47,920 Here's another motivation. 359 00:13:47,920 --> 00:13:51,220 And this is a great example of what I was just talking 360 00:13:51,220 --> 00:13:53,320 about in that potential. 361 00:13:53,320 --> 00:13:57,010 If I have the right potential, and I do my classical force 362 00:13:57,010 --> 00:14:02,350 field calculations, I can feel pretty golden 363 00:14:02,350 --> 00:14:05,500 about simulating the behavior of materials, like how it cracks. 364 00:14:05,500 --> 00:14:07,660 Did you guys do crack propagation? 365 00:14:07,660 --> 00:14:11,180 Ol' Professor Buehler likes crack propagation. 366 00:14:11,180 --> 00:14:13,150 There are not many people on the planet 367 00:14:13,150 --> 00:14:15,910 who more about crack propagation than Professor Buehler. 368 00:14:15,910 --> 00:14:16,840 But look at this. 369 00:14:16,840 --> 00:14:19,090 I've cracked this piece of-- what is this? 370 00:14:19,090 --> 00:14:21,280 Graphene, let's say. 371 00:14:21,280 --> 00:14:21,790 Silicon? 372 00:14:21,790 --> 00:14:22,240 AUDIENCE: Silicon. 373 00:14:22,240 --> 00:14:23,110 JEFFREY GROSSMAN: Oh, it's silicon. 374 00:14:23,110 --> 00:14:24,985 This is silicon just looked at from the side. 375 00:14:24,985 --> 00:14:26,245 Yep, there they are, two. 376 00:14:26,245 --> 00:14:28,640 I've cracked this piece of silicon. 377 00:14:28,640 --> 00:14:32,590 I guess I could have read "silicon" there and known. 378 00:14:32,590 --> 00:14:35,350 And I can't measure it experimentally. 379 00:14:35,350 --> 00:14:37,690 And so I crack it in the computer with something called 380 00:14:37,690 --> 00:14:40,450 an EDIP potential that was fit to certain experimental 381 00:14:40,450 --> 00:14:42,850 parameters, and then I crack it in a computer 382 00:14:42,850 --> 00:14:46,270 with a tight-binding model, and look at the difference. 383 00:14:46,270 --> 00:14:47,620 Is that the same crack? 384 00:14:47,620 --> 00:14:48,770 Is that the same property? 385 00:14:48,770 --> 00:14:50,150 Is it happening in the same way? 386 00:14:50,150 --> 00:14:50,920 Absolutely not. 387 00:14:50,920 --> 00:14:52,510 It's completely different. 388 00:14:52,510 --> 00:14:55,480 Qualitatively, quantitatively, the results you'll get 389 00:14:55,480 --> 00:14:57,850 and the findings you publish will be totally different, 390 00:14:57,850 --> 00:14:59,870 depending on which potential you choose. 391 00:14:59,870 --> 00:15:04,000 So that's really-- this is the reason why 392 00:15:04,000 --> 00:15:06,460 we need these more accurate-- a way, at least, 393 00:15:06,460 --> 00:15:07,900 to get more accurate potentials. 394 00:15:07,900 --> 00:15:10,210 And then you can get these other properties, as I said. 395 00:15:10,210 --> 00:15:14,100 So you can get things like where the electrons are. 396 00:15:14,100 --> 00:15:17,940 You can model things like Raman spectra, which have 397 00:15:17,940 --> 00:15:20,700 to do with electrons and light. 398 00:15:20,700 --> 00:15:24,570 You can model things like reactions. 399 00:15:24,570 --> 00:15:29,310 Now, sometimes potentials-- like especially reacs. 400 00:15:29,310 --> 00:15:31,560 Did you run reacs potentials? 401 00:15:31,560 --> 00:15:37,360 Reacs-- the name "reacs" makes me think reaction. 402 00:15:37,360 --> 00:15:38,570 Does it make you think that? 403 00:15:38,570 --> 00:15:41,170 So they're actually modeled for reactions. 404 00:15:41,170 --> 00:15:42,950 And that means that they can break bonds. 405 00:15:42,950 --> 00:15:45,735 However, there are plenty of reactions-- 406 00:15:45,735 --> 00:15:47,640 AUDIENCE: [SNEEZES] 407 00:15:47,640 --> 00:15:50,700 JEFFREY GROSSMAN: --salute-- where reacs can actually not 408 00:15:50,700 --> 00:15:56,970 get the right physics, the right structure of the potential. 409 00:15:56,970 --> 00:15:57,690 Why? 410 00:15:57,690 --> 00:15:59,340 Well, take a look at this one. 411 00:15:59,340 --> 00:16:03,760 This is butadiene plus ethylene going to cyclohexane-- 412 00:16:03,760 --> 00:16:04,260 hexene. 413 00:16:04,260 --> 00:16:07,890 It's one of the simplest ways you can actually make a ring. 414 00:16:07,890 --> 00:16:08,970 Watch those electrons. 415 00:16:08,970 --> 00:16:14,860 Those are the electrons of the part of the system that's 416 00:16:14,860 --> 00:16:15,860 doing the reaction. 417 00:16:15,860 --> 00:16:17,260 That's where the electrons are. 418 00:16:17,260 --> 00:16:21,280 And where those electrons are is what determines everything 419 00:16:21,280 --> 00:16:27,107 about the reaction-- the barrier, whether it happens. 420 00:16:27,107 --> 00:16:28,690 And let's see if I can get it to play. 421 00:16:28,690 --> 00:16:29,920 And now, watch them. 422 00:16:29,920 --> 00:16:30,430 Watch them. 423 00:16:30,430 --> 00:16:31,840 It's like balloon animals. 424 00:16:31,840 --> 00:16:35,770 See, they pop up on the top, and then they flow across. 425 00:16:35,770 --> 00:16:37,540 And then they do a big shape-shift 426 00:16:37,540 --> 00:16:40,110 as the reaction actually happens, 427 00:16:40,110 --> 00:16:45,250 and they curve back around, and they bubble up on top. 428 00:16:45,250 --> 00:16:49,030 And that's the final position probability of those electrons. 429 00:16:49,030 --> 00:16:51,730 It's a very simple reaction, but the behavior 430 00:16:51,730 --> 00:16:54,730 is extremely complex. 431 00:16:54,730 --> 00:16:59,130 So when you fit a potential, this is what you're ignoring. 432 00:16:59,130 --> 00:17:01,860 All of that complexity. 433 00:17:01,860 --> 00:17:04,050 And you're trying to fit it to some functional form, 434 00:17:04,050 --> 00:17:06,700 and reacs has a whole lot of degrees of freedom, 435 00:17:06,700 --> 00:17:09,329 so it actually can fit some of this complexity very well. 436 00:17:09,329 --> 00:17:12,930 But that just gives you a sense of the kind of thing 437 00:17:12,930 --> 00:17:17,640 that's happening, and why you can miss important aspects 438 00:17:17,640 --> 00:17:19,670 with potentials. 439 00:17:19,670 --> 00:17:23,260 So in the Standard Model, atoms are 440 00:17:23,260 --> 00:17:25,420 made by these massive point-like nuclei. 441 00:17:25,420 --> 00:17:26,990 That's what you've been doing. 442 00:17:26,990 --> 00:17:29,920 And now they're going to be surrounded by these electrons. 443 00:17:29,920 --> 00:17:31,840 And you're going to have core electrons, 444 00:17:31,840 --> 00:17:35,140 and then you're going to have the valence electrons, which 445 00:17:35,140 --> 00:17:36,510 do all the work. 446 00:17:36,510 --> 00:17:38,260 They're the ones that bind together and do 447 00:17:38,260 --> 00:17:40,510 all the interesting stuff. 448 00:17:40,510 --> 00:17:42,820 Somebody tell me, who knows about the chemistry, 449 00:17:42,820 --> 00:17:45,820 like s, p, d filling? 450 00:17:45,820 --> 00:17:47,500 Good. 451 00:17:47,500 --> 00:17:51,632 Somebody tell me, how many electrons are there in carbon? 452 00:17:51,632 --> 00:17:52,467 AUDIENCE: Six. 453 00:17:52,467 --> 00:17:53,050 AUDIENCE: Six. 454 00:17:53,050 --> 00:17:54,880 JEFFREY GROSSMAN: Six. 455 00:17:54,880 --> 00:17:58,520 And how many are core and how many are valence? 456 00:17:58,520 --> 00:17:59,522 What's what there? 457 00:17:59,522 --> 00:18:01,605 AUDIENCE: Two core, two [? valence-- ?] four core, 458 00:18:01,605 --> 00:18:02,290 two valence. 459 00:18:02,290 --> 00:18:05,380 JEFFREY GROSSMAN: OK, so it goes 1s, 2s. 460 00:18:05,380 --> 00:18:07,710 That's four. 461 00:18:07,710 --> 00:18:11,400 2p, how many are in the 2p? 462 00:18:11,400 --> 00:18:13,110 Four, two? 463 00:18:13,110 --> 00:18:14,280 How many? 464 00:18:14,280 --> 00:18:15,060 Two? 465 00:18:15,060 --> 00:18:16,570 Like that, that's good. 466 00:18:16,570 --> 00:18:18,840 Now, what about silicon? 467 00:18:22,760 --> 00:18:24,300 Which number is that? 468 00:18:24,300 --> 00:18:25,340 Oh. 469 00:18:25,340 --> 00:18:27,260 We really like materials-- 470 00:18:27,260 --> 00:18:29,210 material scientists really like silicon. 471 00:18:29,210 --> 00:18:30,500 It's good material. 472 00:18:30,500 --> 00:18:31,490 14. 473 00:18:31,490 --> 00:18:33,455 How many electrons are in the valence? 474 00:18:37,080 --> 00:18:39,690 Yeah, it's the same-- because in carbon-- 475 00:18:39,690 --> 00:18:41,670 you see, you had the 2s and the 2p, 476 00:18:41,670 --> 00:18:44,340 four electrons in the valence. 477 00:18:44,340 --> 00:18:47,700 And in silicon, you've got the 3s and the 3p, 478 00:18:47,700 --> 00:18:49,680 four electrons in the valence. 479 00:18:49,680 --> 00:18:50,670 Right? 480 00:18:50,670 --> 00:18:53,520 But you see, here's carbon. 481 00:18:59,040 --> 00:19:00,780 And here's 2p. 482 00:19:04,162 --> 00:19:05,120 And now here's silicon. 483 00:19:09,480 --> 00:19:13,920 This is 1s, 2s, 2p. 484 00:19:13,920 --> 00:19:16,242 Is this making sense to people? 485 00:19:16,242 --> 00:19:17,700 How many of you have not seen this? 486 00:19:17,700 --> 00:19:19,170 It's OK. 487 00:19:19,170 --> 00:19:20,830 We'll talk a little bit about this. 488 00:19:20,830 --> 00:19:26,090 So these are filled, filled, and so on, up to here. 489 00:19:26,090 --> 00:19:27,590 And then you got these guys. 490 00:19:27,590 --> 00:19:31,310 And this is the valence, and this is the valence. 491 00:19:31,310 --> 00:19:33,920 Those are the electrons that do all of the interacting. 492 00:19:33,920 --> 00:19:36,020 Those are the ones that do the chemical bonding. 493 00:19:36,020 --> 00:19:37,395 They're the ones that we're going 494 00:19:37,395 --> 00:19:40,400 to care about in this class. 495 00:19:40,400 --> 00:19:45,110 We are not going to be working with these core electrons. 496 00:19:45,110 --> 00:19:47,852 Those are core electrons. 497 00:19:47,852 --> 00:19:49,310 So we're going to freeze those out, 498 00:19:49,310 --> 00:19:51,740 because they don't really play much of a role 499 00:19:51,740 --> 00:19:54,380 in the kinds of properties we're going to actually care about 500 00:19:54,380 --> 00:19:55,580 in this class, OK? 501 00:19:58,560 --> 00:20:00,840 And I won't talk much about how we do that. 502 00:20:00,840 --> 00:20:04,650 We do that with something called pseudo potentials, which model 503 00:20:04,650 --> 00:20:07,170 the core part of the electron. 504 00:20:07,170 --> 00:20:09,360 So this part, we're going to get rid of. 505 00:20:09,360 --> 00:20:13,050 Now, somebody tell me why, in looking 506 00:20:13,050 --> 00:20:18,450 at this, why we are made out of carbon and not silicon? 507 00:20:26,580 --> 00:20:29,505 The valence electrons look pretty similar, don't they? 508 00:20:29,505 --> 00:20:34,290 You got a couple of s and a couple of p in each case. 509 00:20:34,290 --> 00:20:35,130 OK, higher. 510 00:20:38,640 --> 00:20:41,108 What does that mean? 511 00:20:41,108 --> 00:20:42,650 AUDIENCE: More metallic [INAUDIBLE].. 512 00:20:42,650 --> 00:20:44,200 JEFFREY GROSSMAN: More metallic? 513 00:20:44,200 --> 00:20:45,345 Maybe. 514 00:20:45,345 --> 00:20:47,418 [? Except so, ?] because I'm metallic. 515 00:20:47,418 --> 00:20:48,507 AUDIENCE: [INAUDIBLE] 516 00:20:48,507 --> 00:20:49,840 JEFFREY GROSSMAN: What was that? 517 00:20:49,840 --> 00:20:50,730 AUDIENCE: More reactive? 518 00:20:50,730 --> 00:20:52,000 JEFFREY GROSSMAN: More active? 519 00:20:52,000 --> 00:20:55,520 Mm, not sure about that. 520 00:20:55,520 --> 00:20:57,945 You could argue that if you think about the alkalis, 521 00:20:57,945 --> 00:21:01,610 if you're thinking in that way, that it wants 522 00:21:01,610 --> 00:21:03,920 to lose these electrons more. 523 00:21:03,920 --> 00:21:07,520 Carbon can be a very reactive atom. 524 00:21:07,520 --> 00:21:11,810 Actually, the bond in diamond is considerably higher energy 525 00:21:11,810 --> 00:21:14,160 than the bond in silicon. 526 00:21:14,160 --> 00:21:16,535 So why are we made out of carbon and not silicon? 527 00:21:16,535 --> 00:21:18,390 We'll come back to that. 528 00:21:18,390 --> 00:21:19,410 Think about it. 529 00:21:19,410 --> 00:21:20,010 It's cheaper? 530 00:21:21,900 --> 00:21:23,520 It's cost-efficient. 531 00:21:23,520 --> 00:21:25,620 Actually, nature is always really good about that. 532 00:21:28,170 --> 00:21:30,210 Not quite the answer. 533 00:21:30,210 --> 00:21:30,900 It's real. 534 00:21:30,900 --> 00:21:34,740 These electrons that we're going to be simulating, they exist! 535 00:21:34,740 --> 00:21:37,890 They can be seen, and look at that complex structure! 536 00:21:37,890 --> 00:21:42,510 That's the complexity of a bond measured in experiment. 537 00:21:42,510 --> 00:21:44,280 That's a real experimental bond. 538 00:21:44,280 --> 00:21:46,440 And it shows where that electron density 539 00:21:46,440 --> 00:21:49,083 is in the bond, and look at how complicated that is. 540 00:21:49,083 --> 00:21:50,500 And that's what I'm talking about. 541 00:21:50,500 --> 00:21:51,780 And we can calculate that-- well, this 542 00:21:51,780 --> 00:21:53,490 is a different material, but you can see 543 00:21:53,490 --> 00:21:55,290 a similar sort of complexity. 544 00:21:55,290 --> 00:21:58,080 We can calculate that complexity with quantum mechanics. 545 00:21:58,080 --> 00:22:01,140 And you can see again by looking at this-- 546 00:22:01,140 --> 00:22:01,710 look at this. 547 00:22:01,710 --> 00:22:04,200 I mean, there's like a ball underneath a donut 548 00:22:04,200 --> 00:22:08,540 and a teardrop, and a donut and a ball. 549 00:22:08,540 --> 00:22:11,270 Did your classical potential get all of that? 550 00:22:11,270 --> 00:22:11,990 No way. 551 00:22:11,990 --> 00:22:15,260 It's just averaging over this, right? 552 00:22:15,260 --> 00:22:19,490 And so once we go to trying to calculate properties 553 00:22:19,490 --> 00:22:22,580 of materials that are this complex, electrons, 554 00:22:22,580 --> 00:22:24,318 we really got to get it right. 555 00:22:24,318 --> 00:22:26,360 And that's what the Schrodinger equation will do. 556 00:22:26,360 --> 00:22:31,730 So now, why is this important to solve in the computer? 557 00:22:31,730 --> 00:22:34,640 Well, it's sort of the same reasons for-- 558 00:22:34,640 --> 00:22:37,100 these are the same reasons for classical, 559 00:22:37,100 --> 00:22:39,180 the first part of the class. 560 00:22:39,180 --> 00:22:41,330 It provides us with a microscopic understanding. 561 00:22:41,330 --> 00:22:42,980 It has predictive power. 562 00:22:42,980 --> 00:22:46,220 And in this case, we can really say it's first-principles. 563 00:22:46,220 --> 00:22:49,010 And you hear this word "first-principles--" 564 00:22:49,010 --> 00:22:50,960 how many of you have had "first-principles?" 565 00:22:50,960 --> 00:22:51,710 What does it mean? 566 00:22:55,200 --> 00:22:56,205 Take a guess. 567 00:22:56,205 --> 00:22:58,320 AUDIENCE: From the basic-- 568 00:22:58,320 --> 00:23:00,288 just from basic axiom. 569 00:23:00,288 --> 00:23:01,830 You're not really assuming very much. 570 00:23:01,830 --> 00:23:03,240 JEFFREY GROSSMAN: Exactly. 571 00:23:03,240 --> 00:23:05,460 And in this case, what are we going to assume? 572 00:23:05,460 --> 00:23:07,680 What is the only input into the simulation? 573 00:23:07,680 --> 00:23:08,685 AUDIENCE: [INAUDIBLE] 574 00:23:08,685 --> 00:23:10,560 JEFFREY GROSSMAN: Well, what's the only input 575 00:23:10,560 --> 00:23:12,270 into the simulation of that equation? 576 00:23:12,270 --> 00:23:14,520 AUDIENCE: [INAUDIBLE] 577 00:23:14,520 --> 00:23:16,604 JEFFREY GROSSMAN: The atom what? 578 00:23:16,604 --> 00:23:18,356 AUDIENCE: Like the atom that you're-- 579 00:23:18,356 --> 00:23:20,150 JEFFREY GROSSMAN: Yeah, which is what? 580 00:23:20,150 --> 00:23:23,060 Just the atom. 581 00:23:23,060 --> 00:23:23,870 The atom number. 582 00:23:23,870 --> 00:23:25,130 And maybe its position. 583 00:23:25,130 --> 00:23:26,210 That's important. 584 00:23:26,210 --> 00:23:28,580 Like where the atom is. 585 00:23:28,580 --> 00:23:29,632 And the charge. 586 00:23:29,632 --> 00:23:30,590 The charge on the atom. 587 00:23:30,590 --> 00:23:32,450 Is it ionized, is it not. 588 00:23:32,450 --> 00:23:35,000 And that's it. 589 00:23:35,000 --> 00:23:38,060 Not really, ha, because we have to make approximations. 590 00:23:38,060 --> 00:23:41,450 But ideally, that's all we would need to put in 591 00:23:41,450 --> 00:23:44,180 to solve first-principles. 592 00:23:44,180 --> 00:23:47,120 That is, to solve without any other fits or inputs. 593 00:23:47,120 --> 00:23:49,160 Just the atom, which atom is it, and where is it 594 00:23:49,160 --> 00:23:51,180 is what you put in. 595 00:23:51,180 --> 00:23:54,840 And the challenges we have is that this 596 00:23:54,840 --> 00:23:57,510 is a much more computationally-intensive kind 597 00:23:57,510 --> 00:23:58,180 of simulation. 598 00:23:58,180 --> 00:24:01,590 So how long-- who was saying that it was too long? 599 00:24:01,590 --> 00:24:03,330 And then we'll have classical-- 600 00:24:03,330 --> 00:24:05,110 yeah, how long was it taken? 601 00:24:05,110 --> 00:24:06,090 AUDIENCE: Six hours. 602 00:24:06,090 --> 00:24:09,420 JEFFREY GROSSMAN: Six hours, and how many atoms? 603 00:24:09,420 --> 00:24:10,320 AUDIENCE: One-- 604 00:24:10,320 --> 00:24:11,673 JEFFREY GROSSMAN: One atom? 605 00:24:11,673 --> 00:24:13,026 AUDIENCE: No, 150,000. 606 00:24:13,026 --> 00:24:14,280 JEFFREY GROSSMAN: Oh, 150,000. 607 00:24:14,280 --> 00:24:15,750 OK, good. 608 00:24:15,750 --> 00:24:19,980 So if we tried to simulate 150,000 atoms, that's not even 609 00:24:19,980 --> 00:24:21,060 a sentence I can start. 610 00:24:21,060 --> 00:24:22,610 Actually, in quantum mechanics, you 611 00:24:22,610 --> 00:24:24,220 can't even get close to that. 612 00:24:24,220 --> 00:24:27,840 So if you try to do 150 atoms in quantum mechanics, 613 00:24:27,840 --> 00:24:29,610 it could easily take you six hours, 614 00:24:29,610 --> 00:24:33,095 and it could take you even much more. 615 00:24:33,095 --> 00:24:34,470 Our goal in the homeworks will be 616 00:24:34,470 --> 00:24:38,200 to make sure the simulations take as long as possible. 617 00:24:38,200 --> 00:24:39,237 I'm kidding. 618 00:24:39,237 --> 00:24:41,320 But we'll make sure that they don't take too long. 619 00:24:41,320 --> 00:24:43,883 But they're slow and painful, and you will feel that pain. 620 00:24:43,883 --> 00:24:45,550 Not because we're going to make problems 621 00:24:45,550 --> 00:24:47,380 where you have to simulate for a long time, 622 00:24:47,380 --> 00:24:49,870 but because you'll just see. 623 00:24:49,870 --> 00:24:53,140 You'll be like, wait a second, I only got two atoms in here. 624 00:24:53,140 --> 00:24:54,940 Why does this take an hour? 625 00:24:54,940 --> 00:24:57,715 Well, it's because even with all the approximations 626 00:24:57,715 --> 00:25:00,070 and the computer speed, it just takes 627 00:25:00,070 --> 00:25:01,870 longer to do these kinds of calculations 628 00:25:01,870 --> 00:25:04,000 that are more complex. 629 00:25:04,000 --> 00:25:06,170 OK? 630 00:25:06,170 --> 00:25:09,030 How many people know where the fastest computer in the world 631 00:25:09,030 --> 00:25:09,530 is? 632 00:25:09,530 --> 00:25:11,420 I asked this question already. 633 00:25:11,420 --> 00:25:13,410 You know the answer. 634 00:25:13,410 --> 00:25:13,910 Where is it? 635 00:25:13,910 --> 00:25:14,225 AUDIENCE: Google. 636 00:25:14,225 --> 00:25:15,302 JEFFREY GROSSMAN: Google. 637 00:25:15,302 --> 00:25:16,760 How many people know how many times 638 00:25:16,760 --> 00:25:19,880 I've asked them for an account? 639 00:25:19,880 --> 00:25:20,960 It's many. 640 00:25:20,960 --> 00:25:23,090 They never gave it to me. 641 00:25:23,090 --> 00:25:25,160 I would love to run on Google's computer. 642 00:25:25,160 --> 00:25:28,160 OK, classical mechanics goes back a long way. 643 00:25:28,160 --> 00:25:29,820 This is what you've been solving. 644 00:25:29,820 --> 00:25:32,950 You've been doing a lot of F equals ma. 645 00:25:32,950 --> 00:25:37,412 And there are problems with it that led to quantum mechanics. 646 00:25:37,412 --> 00:25:39,370 I'm just going to give you a couple of examples 647 00:25:39,370 --> 00:25:41,110 because they're fun, and then I'm 648 00:25:41,110 --> 00:25:44,640 going to show you a really goofy movie. 649 00:25:44,640 --> 00:25:46,770 Has anybody seen the really goofy quantum movie 650 00:25:46,770 --> 00:25:47,728 that I'm going to show? 651 00:25:47,728 --> 00:25:48,895 AUDIENCE: Is it Dr. Quantum? 652 00:25:48,895 --> 00:25:51,660 JEFFREY GROSSMAN: It's not Dr. Quantum, but that sounds cool. 653 00:25:51,660 --> 00:25:55,990 Maybe it's Dr. Quan-- no, I don't think it's Dr. Quantum. 654 00:25:55,990 --> 00:25:59,080 Has anybody seen really goofy quantum movies? 655 00:25:59,080 --> 00:26:00,220 I love goofy movies. 656 00:26:00,220 --> 00:26:04,630 If you had me for 3012, you know I like strange movies. 657 00:26:04,630 --> 00:26:06,960 It's a little thing. 658 00:26:06,960 --> 00:26:08,710 And they're just a couple, so I promise 659 00:26:08,710 --> 00:26:09,877 you there won't be too many. 660 00:26:09,877 --> 00:26:14,170 One I'll show you today, and one I'll show you on Thursday. 661 00:26:14,170 --> 00:26:17,680 Some of the problems that led to the need 662 00:26:17,680 --> 00:26:20,530 to develop a new theory were the classical atom, 663 00:26:20,530 --> 00:26:25,100 the quantization of properties, the wave aspect of matter. 664 00:26:25,100 --> 00:26:27,220 We'll talk about those. 665 00:26:27,220 --> 00:26:29,862 And then black-body radiation, which I won't talk about, 666 00:26:29,862 --> 00:26:32,070 but that's a really cool one because of the word they 667 00:26:32,070 --> 00:26:34,710 use to describe the failure. 668 00:26:34,710 --> 00:26:37,650 How many people know what I'm talking about? 669 00:26:37,650 --> 00:26:39,468 It's called the ultraviolet-- 670 00:26:39,468 --> 00:26:40,385 AUDIENCE: Catastrophe? 671 00:26:40,385 --> 00:26:43,120 JEFFREY GROSSMAN: Catastrophe! 672 00:26:43,120 --> 00:26:44,740 I love it. 673 00:26:44,740 --> 00:26:48,470 You can't really call theories today a catastrophe. 674 00:26:48,470 --> 00:26:52,180 You got to have a lot of-- but that was a catastrophe. 675 00:26:52,180 --> 00:26:53,770 That was really a catastrophe. 676 00:26:53,770 --> 00:26:56,230 Because the energy that was going 677 00:26:56,230 --> 00:26:58,660 to be emitted from a black body just kept going up and up 678 00:26:58,660 --> 00:26:59,860 and up and up. 679 00:26:59,860 --> 00:27:02,200 And it doesn't do that in experiment. 680 00:27:02,200 --> 00:27:04,050 That's a catastrophe. 681 00:27:04,050 --> 00:27:05,800 Catastrophe, when you use words like that, 682 00:27:05,800 --> 00:27:07,210 you know you need a new theory. 683 00:27:12,050 --> 00:27:15,980 A lot of really, really, really smart people 684 00:27:15,980 --> 00:27:17,540 were thinking about these problems. 685 00:27:17,540 --> 00:27:18,830 They were aware of them. 686 00:27:18,830 --> 00:27:22,010 They knew they had these problems back at the time. 687 00:27:22,010 --> 00:27:24,350 And they were really working intensely 688 00:27:24,350 --> 00:27:28,290 on saying, well, why are we having all these problems 689 00:27:28,290 --> 00:27:30,300 describing the world? 690 00:27:30,300 --> 00:27:33,450 We've been good to go for 400 years. 691 00:27:33,450 --> 00:27:34,350 And now this? 692 00:27:34,350 --> 00:27:36,500 350 years. 693 00:27:36,500 --> 00:27:37,280 What's going on? 694 00:27:39,800 --> 00:27:43,670 In the classical atom, the problem there is that, you see, 695 00:27:43,670 --> 00:27:45,860 if you think about a hydrogen atom 696 00:27:45,860 --> 00:27:49,430 as a plus charge surrounded by a negative charge-- that's 697 00:27:49,430 --> 00:27:52,250 the nucleus, and there's the proton, 698 00:27:52,250 --> 00:27:54,180 and there's the electron. 699 00:27:54,180 --> 00:27:58,670 And if it's orbiting, then it has to be accelerating. 700 00:27:58,670 --> 00:28:01,760 And we know that an accelerating charge 701 00:28:01,760 --> 00:28:04,800 is going to give off energy in the form of radiation. 702 00:28:04,800 --> 00:28:05,300 Right? 703 00:28:07,930 --> 00:28:10,950 Well, if that were true-- 704 00:28:10,950 --> 00:28:12,480 and we know it is true. 705 00:28:12,480 --> 00:28:16,420 In some situations, they knew it very well to be true. 706 00:28:16,420 --> 00:28:19,690 That's what a synchrotron is. 707 00:28:19,690 --> 00:28:22,840 But then this should just spiral, right? 708 00:28:22,840 --> 00:28:27,310 And it should just collapse into the center here. 709 00:28:27,310 --> 00:28:29,350 Why doesn't it do that? 710 00:28:29,350 --> 00:28:32,920 Do you know how long a hydrogen atom should be stable, 711 00:28:32,920 --> 00:28:36,400 according to that classical world, that classical picture 712 00:28:36,400 --> 00:28:37,672 of accelerating charge? 713 00:28:37,672 --> 00:28:39,130 It's accelerating, by the way, just 714 00:28:39,130 --> 00:28:42,040 to stay on course around this circle. 715 00:28:42,040 --> 00:28:44,850 So it's giving off radiation, losing energy, 716 00:28:44,850 --> 00:28:45,742 meaning its orbit-- 717 00:28:45,742 --> 00:28:47,700 it should come closer and closer to the center. 718 00:28:47,700 --> 00:28:49,216 How long would that be stable? 719 00:28:49,216 --> 00:28:50,091 AUDIENCE: [INAUDIBLE] 720 00:28:50,091 --> 00:28:52,170 JEFFREY GROSSMAN: What fraction? 721 00:28:52,170 --> 00:28:54,383 Give me a 10 to the minus something. 722 00:28:54,383 --> 00:28:55,208 AUDIENCE: 12. 723 00:28:55,208 --> 00:28:57,000 JEFFREY GROSSMAN: Yeah, right around there. 724 00:28:57,000 --> 00:28:59,130 10 to the minus 10, 10 to the minus 12. 725 00:28:59,130 --> 00:29:02,250 That's how long hydrogen atoms would be in existence 726 00:29:02,250 --> 00:29:06,760 if classical physics described them, which it doesn't. 727 00:29:06,760 --> 00:29:09,040 And then there was this. 728 00:29:09,040 --> 00:29:12,190 And this was a really cool thing that 729 00:29:12,190 --> 00:29:17,245 also could not be described by the classical world. 730 00:29:19,850 --> 00:29:24,550 And again, this is my reduced Shakespeare version of quantum, 731 00:29:24,550 --> 00:29:28,210 so we're covering these very general, very interesting 732 00:29:28,210 --> 00:29:32,080 topics just to give you a flavor and a feeling. 733 00:29:32,080 --> 00:29:33,913 And then, if you want to learn more, 734 00:29:33,913 --> 00:29:35,830 there's just so much you can read about these. 735 00:29:35,830 --> 00:29:38,320 They're really cool experiments that were done. 736 00:29:38,320 --> 00:29:41,980 This is the experiment that won Einstein the Nobel Prize. 737 00:29:44,740 --> 00:29:47,050 It's very important work, but it's probably 738 00:29:47,050 --> 00:29:50,380 one of his least profound pieces of work. 739 00:29:50,380 --> 00:29:54,250 But it was very important, again, 740 00:29:54,250 --> 00:29:56,950 to start to understand this duality between waves 741 00:29:56,950 --> 00:29:59,800 and particles, which I'll talk about in a few minutes. 742 00:29:59,800 --> 00:30:04,150 And what he found is that if you take a piece of metal, 743 00:30:04,150 --> 00:30:07,510 and you shine a light on it, the energy from the light 744 00:30:07,510 --> 00:30:11,220 can kick electrons out. 745 00:30:11,220 --> 00:30:14,040 But what was thought is that if you increase 746 00:30:14,040 --> 00:30:18,240 the intensity of the light, that you'd 747 00:30:18,240 --> 00:30:22,230 increase how much energy these particles get kicked out by. 748 00:30:22,230 --> 00:30:26,400 You just increase the intensity of the light, 749 00:30:26,400 --> 00:30:30,600 and then you could get these things to come out 750 00:30:30,600 --> 00:30:32,790 at higher and higher energies. 751 00:30:32,790 --> 00:30:37,230 But if you plot the energy of an electron coming out 752 00:30:37,230 --> 00:30:40,560 of the metal versus the intensity of the light, 753 00:30:40,560 --> 00:30:41,745 it's a flat line. 754 00:30:41,745 --> 00:30:43,620 It does not depend on the intensity of light. 755 00:30:43,620 --> 00:30:46,710 You get more electrons out, but you don't get 756 00:30:46,710 --> 00:30:49,900 them to be any more energetic. 757 00:30:49,900 --> 00:30:55,350 And that had to lead to a picture of light 758 00:30:55,350 --> 00:30:59,620 not necessarily being a wave. 759 00:30:59,620 --> 00:31:02,020 Because instead, what you find is 760 00:31:02,020 --> 00:31:04,720 that there is this very strong direct dependence 761 00:31:04,720 --> 00:31:06,640 of the energy of the electrons that come out 762 00:31:06,640 --> 00:31:08,650 when you shine light on a piece of metal, 763 00:31:08,650 --> 00:31:11,560 and the frequency of the light. 764 00:31:11,560 --> 00:31:14,550 And so what Einstein said is, well, maybe light 765 00:31:14,550 --> 00:31:20,080 can be thought of as particles that have an energy that 766 00:31:20,080 --> 00:31:22,030 depends on their frequency. 767 00:31:22,030 --> 00:31:25,180 And he wrote this thing down. 768 00:31:25,180 --> 00:31:27,010 So they have an energy that depends 769 00:31:27,010 --> 00:31:31,360 on this Planck's constant, this thing here, this h, or h bar. 770 00:31:31,360 --> 00:31:32,650 Do you like a bar, do you not? 771 00:31:32,650 --> 00:31:34,780 Do you like pi? 772 00:31:34,780 --> 00:31:36,940 Do you like 2 pi Do you want to write that, not? 773 00:31:36,940 --> 00:31:42,640 This is all-- it's a free world, and you guys can write h or h 774 00:31:42,640 --> 00:31:44,725 bar, however you want. 775 00:31:44,725 --> 00:31:45,850 That's my feeling about it. 776 00:31:45,850 --> 00:31:48,060 I'll stop there. 777 00:31:48,060 --> 00:31:49,600 h bar. 778 00:31:49,600 --> 00:31:51,280 h. 779 00:31:51,280 --> 00:31:56,840 2 pi But you'll need to get it right for solving problems, 780 00:31:56,840 --> 00:31:58,430 right? 781 00:31:58,430 --> 00:32:00,590 But this is the energy, and it's quantized. 782 00:32:00,590 --> 00:32:02,270 Well, no, sorry, it's not quantized yet. 783 00:32:02,270 --> 00:32:03,350 I didn't say that. 784 00:32:03,350 --> 00:32:04,640 But it's a particle. 785 00:32:04,640 --> 00:32:06,170 It's based on the frequency. 786 00:32:06,170 --> 00:32:09,380 The energy goes as the frequency of the light, 787 00:32:09,380 --> 00:32:11,830 and that's what was measured. 788 00:32:11,830 --> 00:32:14,690 Kind of building on the understanding of what's 789 00:32:14,690 --> 00:32:16,280 going on. 790 00:32:16,280 --> 00:32:18,650 And this is a great one. 791 00:32:18,650 --> 00:32:23,210 When you look out-- you see, if you excite an atom, 792 00:32:23,210 --> 00:32:25,960 if you excite the electron in an atom, 793 00:32:25,960 --> 00:32:28,130 and you let it go back down-- 794 00:32:28,130 --> 00:32:33,880 so if you excite an electron, let's say of a hydrogen atom. 795 00:32:33,880 --> 00:32:36,610 Here's your hydrogen atom, and here's 796 00:32:36,610 --> 00:32:37,930 that electron that's orbiting. 797 00:32:37,930 --> 00:32:41,290 It's not orbiting, but we're going to say it's orbiting. 798 00:32:41,290 --> 00:32:45,280 And you excite it up in energy, and then it goes back down, 799 00:32:45,280 --> 00:32:47,790 it emits light. 800 00:32:47,790 --> 00:32:51,040 And so you can look out into the world-- 801 00:32:51,040 --> 00:32:53,730 which is whole lot of hydrogen-- 802 00:32:53,730 --> 00:32:58,110 and you can say, well, what kind of light do I see? 803 00:32:58,110 --> 00:33:01,823 And you would think, according to classical physics, 804 00:33:01,823 --> 00:33:03,240 the classical world said, well, it 805 00:33:03,240 --> 00:33:05,820 could be excited to any amount from different reasons, 806 00:33:05,820 --> 00:33:07,140 can excite an electron. 807 00:33:07,140 --> 00:33:09,130 We won't talk about that now. 808 00:33:09,130 --> 00:33:12,790 Instead, you look out, and you see what wavelengths of light 809 00:33:12,790 --> 00:33:15,520 are coming at you from hydrogen and space, 810 00:33:15,520 --> 00:33:19,750 and you don't see a continuous spectrum at all. 811 00:33:19,750 --> 00:33:23,200 You see only very, very certain wavelengths. 812 00:33:23,200 --> 00:33:24,580 So why? 813 00:33:24,580 --> 00:33:25,960 How could that possibly be? 814 00:33:29,530 --> 00:33:33,220 That was-- now we say, well, it's just quantization. 815 00:33:33,220 --> 00:33:36,500 Particle in a box, which I'll get to in a second. 816 00:33:36,500 --> 00:33:39,370 But back then, they didn't have particle in a box. 817 00:33:39,370 --> 00:33:40,840 They didn't have Schrodinger. 818 00:33:40,840 --> 00:33:43,570 They didn't even really know whether light was 819 00:33:43,570 --> 00:33:46,030 a particle, a wave, or what. 820 00:33:46,030 --> 00:33:49,630 They were really grappling with that. 821 00:33:49,630 --> 00:33:54,310 Now-- and it actually is even more complex, 822 00:33:54,310 --> 00:33:57,860 and we'll see this complexity in the next couple lectures. 823 00:33:57,860 --> 00:34:01,180 We'll be able to actually calculate this if we want, 824 00:34:01,180 --> 00:34:04,330 than just those discrete energies. 825 00:34:04,330 --> 00:34:06,160 There were these big jumps, and then there 826 00:34:06,160 --> 00:34:08,020 were these little jumps. 827 00:34:08,020 --> 00:34:11,117 What's up with that? 828 00:34:11,117 --> 00:34:12,659 They didn't just see discrete things, 829 00:34:12,659 --> 00:34:14,969 they saw them sort of bundled up. 830 00:34:14,969 --> 00:34:17,790 And then, if you were lucky enough 831 00:34:17,790 --> 00:34:20,460 to have looked at one of these series, 832 00:34:20,460 --> 00:34:24,480 and you were like, a-ha, I got the green one, 833 00:34:24,480 --> 00:34:27,090 then you got it to be named after you, if it was 834 00:34:27,090 --> 00:34:28,870 one of the first five or six. 835 00:34:28,870 --> 00:34:30,179 And that's why they have names. 836 00:34:30,179 --> 00:34:32,596 And then they stopped naming them, because they were like, 837 00:34:32,596 --> 00:34:34,320 well, OK, we kind of get it already. 838 00:34:34,320 --> 00:34:36,960 Like, I don't know if there's a name for the sixth one. 839 00:34:36,960 --> 00:34:38,600 Maybe there is. 840 00:34:38,600 --> 00:34:39,540 Does anybody know? 841 00:34:39,540 --> 00:34:40,040 Yeah. 842 00:34:40,040 --> 00:34:42,116 AUDIENCE: [INAUDIBLE] 843 00:34:42,116 --> 00:34:44,449 JEFFREY GROSSMAN: See, now, I could take that as ageism, 844 00:34:44,449 --> 00:34:45,830 but I won't. 845 00:34:45,830 --> 00:34:51,020 Because, now-- I'm kidding. 846 00:34:51,020 --> 00:34:54,080 My group makes fun of my age very often. 847 00:34:54,080 --> 00:34:58,860 Now, OK. 848 00:34:58,860 --> 00:35:00,720 This is the time to put down your PDAs-- 849 00:35:00,720 --> 00:35:03,060 if you're in the back and looking at them-- 850 00:35:03,060 --> 00:35:05,760 and to pay attention, because this is a really fun movie 851 00:35:05,760 --> 00:35:08,010 and I wouldn't want you to miss it just because you're 852 00:35:08,010 --> 00:35:09,766 texting somebody. 853 00:35:09,766 --> 00:35:10,712 [VIDEO PLAYBACK] 854 00:35:10,712 --> 00:35:11,660 - And here we are. 855 00:35:11,660 --> 00:35:12,410 JEFFREY GROSSMAN: Is that quantum guy? 856 00:35:12,410 --> 00:35:12,910 OK. 857 00:35:12,910 --> 00:35:15,560 - Granddaddy of all quantum weirdness-- 858 00:35:15,560 --> 00:35:17,233 the infamous double slit experiment. 859 00:35:17,233 --> 00:35:19,400 JEFFREY GROSSMAN: Got to know about the double slit. 860 00:35:19,400 --> 00:35:21,140 - To understand this experiment, we first 861 00:35:21,140 --> 00:35:27,020 need to see how particles, or little balls of matter, act. 862 00:35:27,020 --> 00:35:29,890 If we randomly shoot a small object-- 863 00:35:29,890 --> 00:35:33,260 say, a marble-- at the screen, we 864 00:35:33,260 --> 00:35:35,780 see a pattern on the back wall where they 865 00:35:35,780 --> 00:35:38,630 went through the slit and hit. 866 00:35:38,630 --> 00:35:42,380 Now, if we add a second slit, we would 867 00:35:42,380 --> 00:35:46,360 expect to see a second band duplicated to the right. 868 00:35:49,050 --> 00:35:52,570 Now let's look at waves. 869 00:35:52,570 --> 00:35:56,330 The waves hit the slit and radiate out, 870 00:35:56,330 --> 00:36:00,140 striking the back wall with the most intensity 871 00:36:00,140 --> 00:36:03,560 directly in line with the slit. 872 00:36:03,560 --> 00:36:06,380 The line of brightness on the back screen 873 00:36:06,380 --> 00:36:08,710 shows that intensity. 874 00:36:08,710 --> 00:36:12,180 This is similar to the line the marbles make. 875 00:36:12,180 --> 00:36:19,560 But when we add the second slit, something different happens. 876 00:36:19,560 --> 00:36:24,750 If the top of one wave meets the bottom of another wave, 877 00:36:24,750 --> 00:36:27,420 they cancel each other out. 878 00:36:27,420 --> 00:36:32,190 So now there is an interference pattern on the back wall. 879 00:36:32,190 --> 00:36:36,570 Places where the two tops meet are the highest intensity-- 880 00:36:36,570 --> 00:36:40,750 the bright lines-- and where they cancel, there is nothing. 881 00:36:40,750 --> 00:36:43,800 So when we throw things-- 882 00:36:43,800 --> 00:36:48,690 that is, matter-- through two slits, we get this-- 883 00:36:48,690 --> 00:36:52,560 two bands of [? hits. ?] And with waves, 884 00:36:52,560 --> 00:36:57,190 we get an interference pattern of many bands. 885 00:36:57,190 --> 00:36:58,780 Good, so far. 886 00:36:58,780 --> 00:37:03,030 Now let's go quantum. 887 00:37:03,030 --> 00:37:06,820 JEFFREY GROSSMAN: Now that's what I'm talking about. 888 00:37:06,820 --> 00:37:11,950 - An electron is a tiny, tiny bit of matter, 889 00:37:11,950 --> 00:37:14,310 like a tiny marble. 890 00:37:14,310 --> 00:37:18,060 Let's fire a stream through one slit. 891 00:37:18,060 --> 00:37:20,190 It behaves just like the marble-- 892 00:37:20,190 --> 00:37:22,850 a single band. 893 00:37:22,850 --> 00:37:27,380 So if we shoot these tiny bits through two slits, 894 00:37:27,380 --> 00:37:32,320 we should get, like the marbles, two bands. 895 00:37:32,320 --> 00:37:33,820 What? 896 00:37:33,820 --> 00:37:36,070 An interference pattern! 897 00:37:36,070 --> 00:37:40,480 We fired electrons, tiny bits of matter through, 898 00:37:40,480 --> 00:37:45,430 and we get a pattern like waves, not like little marbles. 899 00:37:45,430 --> 00:37:46,915 How? 900 00:37:46,915 --> 00:37:50,860 How could pieces of matter create an interference pattern 901 00:37:50,860 --> 00:37:52,570 like a wave? 902 00:37:52,570 --> 00:37:54,880 It doesn't make sense. 903 00:37:54,880 --> 00:37:57,580 But physicists are clever. 904 00:37:57,580 --> 00:38:00,370 They thought, maybe those little balls 905 00:38:00,370 --> 00:38:04,120 are bouncing off each other and creating that pattern. 906 00:38:04,120 --> 00:38:08,140 So they decide to shoot electrons through one 907 00:38:08,140 --> 00:38:08,920 at a time. 908 00:38:08,920 --> 00:38:10,212 JEFFREY GROSSMAN: This is cool. 909 00:38:10,212 --> 00:38:13,920 - There is no way they can interfere with each other. 910 00:38:13,920 --> 00:38:17,370 But after an hour of this, the same interference pattern 911 00:38:17,370 --> 00:38:18,780 is seen to emerge. 912 00:38:18,780 --> 00:38:21,690 The conclusion is inescapable. 913 00:38:21,690 --> 00:38:24,770 The single electron leaves as a particle, 914 00:38:24,770 --> 00:38:28,740 becomes a wave of potentials, goes through both slits, 915 00:38:28,740 --> 00:38:33,650 and interferes with itself to hit the wall like a particle. 916 00:38:33,650 --> 00:38:36,140 But mathematically, it's even stranger. 917 00:38:36,140 --> 00:38:40,070 It goes through both slits, and it goes through neither, 918 00:38:40,070 --> 00:38:42,140 and it goes through just one, and it 919 00:38:42,140 --> 00:38:44,040 goes through just the other. 920 00:38:44,040 --> 00:38:47,120 All of these possibilities are in superposition 921 00:38:47,120 --> 00:38:48,110 with each other. 922 00:38:48,110 --> 00:38:51,030 But physicists were completely baffled by this, 923 00:38:51,030 --> 00:38:54,130 so they decided to peek and see which 924 00:38:54,130 --> 00:38:57,770 slit it actually goes through. 925 00:38:57,770 --> 00:39:00,750 And they put a measuring device by one slit 926 00:39:00,750 --> 00:39:03,960 to see which one it went through and let it fly. 927 00:39:05,970 --> 00:39:09,300 But the quantum world is far more mysterious 928 00:39:09,300 --> 00:39:11,310 than they could have imagined. 929 00:39:11,310 --> 00:39:15,030 When they observed, the electron went back 930 00:39:15,030 --> 00:39:17,040 to behaving like a little marble! 931 00:39:17,040 --> 00:39:21,510 It produced a pattern of two bands, not an interference 932 00:39:21,510 --> 00:39:23,550 pattern of many. 933 00:39:23,550 --> 00:39:28,740 The very act of measuring, or observing, 934 00:39:28,740 --> 00:39:31,680 which slit it went through meant it only 935 00:39:31,680 --> 00:39:35,180 went through one, not both. 936 00:39:35,180 --> 00:39:40,421 The electron decided to act differently, 937 00:39:40,421 --> 00:39:43,820 as though it was aware it was being watched. 938 00:39:45,350 --> 00:39:49,100 And it was here that physicists stepped forever 939 00:39:49,100 --> 00:39:53,510 into the strange neverworld of quantum events. 940 00:39:53,510 --> 00:39:57,920 What is matter-- marbles or waves? 941 00:39:57,920 --> 00:40:00,180 And waves of what? 942 00:40:00,180 --> 00:40:05,575 And what does an observer have to do with any of this? 943 00:40:05,575 --> 00:40:13,437 The observer collapsed the wave function simply by observing. 944 00:40:13,437 --> 00:40:14,750 [END PLAYBACK] 945 00:40:14,750 --> 00:40:16,270 JEFFREY GROSSMAN: Nice. 946 00:40:16,270 --> 00:40:17,210 That's pretty cool. 947 00:40:17,210 --> 00:40:19,610 I mean, it's a little bit-- 948 00:40:19,610 --> 00:40:23,210 but does that blow you away? 949 00:40:23,210 --> 00:40:23,810 Seriously? 950 00:40:23,810 --> 00:40:27,170 I mean, I-- so here's the thing. 951 00:40:27,170 --> 00:40:29,780 I strongly recommend you take this movie 952 00:40:29,780 --> 00:40:33,590 out the next time you go to a bar, 953 00:40:33,590 --> 00:40:36,710 and when you're at the table, maybe you're 954 00:40:36,710 --> 00:40:37,910 on your second round-- 955 00:40:37,910 --> 00:40:39,390 wait, I keep doing this. 956 00:40:39,390 --> 00:40:41,165 You guys shouldn't be drinking. 957 00:40:41,165 --> 00:40:42,470 Sorry. 958 00:40:42,470 --> 00:40:44,000 I keep making this mistake. 959 00:40:44,000 --> 00:40:47,732 OK, you're drinking tomato juice, 960 00:40:47,732 --> 00:40:49,190 and you bust out this movie, you're 961 00:40:49,190 --> 00:40:50,360 going to blow people away. 962 00:40:50,360 --> 00:40:51,990 And it's a really great-- 963 00:40:51,990 --> 00:40:58,107 it's a conversation starter, it's an ice breaker. 964 00:40:58,107 --> 00:40:59,690 And that's why Niels Bohr said "anyone 965 00:40:59,690 --> 00:41:02,270 who is not shocked by quantum theory has not understood it." 966 00:41:02,270 --> 00:41:05,130 And here's what's amazing about it. 967 00:41:05,130 --> 00:41:10,780 This is real stuff that matters a lot for material science 968 00:41:10,780 --> 00:41:13,970 and every other discipline in engineering. 969 00:41:13,970 --> 00:41:19,215 This is not just some theoretical, very super 970 00:41:19,215 --> 00:41:24,110 physics-y, probably not going to matter to me kind of thing. 971 00:41:24,110 --> 00:41:26,790 Well, this matters a lot, because this 972 00:41:26,790 --> 00:41:28,420 is how electrons behave. 973 00:41:32,110 --> 00:41:34,055 And that's what, as I said, dictates 974 00:41:34,055 --> 00:41:35,680 so many of the properties and materials 975 00:41:35,680 --> 00:41:37,300 that we care about, especially in energy, 976 00:41:37,300 --> 00:41:39,880 which we'll spend some time in this part of the class talking 977 00:41:39,880 --> 00:41:41,500 about. 978 00:41:41,500 --> 00:41:44,740 So I got to talk about Schrodinger's cat. 979 00:41:44,740 --> 00:41:47,680 How many of you know about Schrodinger's cat? 980 00:41:47,680 --> 00:41:51,560 Who can tell me what you do with this poor guy? 981 00:41:51,560 --> 00:41:52,580 Go ahead. 982 00:41:52,580 --> 00:41:55,063 Somebody-- who said they knew about Schrodinger's cat? 983 00:41:55,063 --> 00:41:55,980 What's the experiment? 984 00:41:55,980 --> 00:41:56,960 Yeah. 985 00:41:56,960 --> 00:41:58,870 AUDIENCE: So you put a cat in the box, and-- 986 00:41:58,870 --> 00:42:00,990 JEFFREY GROSSMAN: Put a cat in a box. 987 00:42:00,990 --> 00:42:05,850 AUDIENCE: And you have some sort of radioactive element, or-- 988 00:42:05,850 --> 00:42:07,100 JEFFREY GROSSMAN: Radioactive. 989 00:42:07,100 --> 00:42:10,100 AUDIENCE: --Schrodinger liked to particle, or whatever. 990 00:42:10,100 --> 00:42:14,900 And you have a Geiger counter or something to measure it that 991 00:42:14,900 --> 00:42:18,260 will break a vial of poison if it detects the radiation 992 00:42:18,260 --> 00:42:19,300 and won't if it doesn't. 993 00:42:19,300 --> 00:42:20,300 JEFFREY GROSSMAN: Right. 994 00:42:20,300 --> 00:42:25,442 AUDIENCE: And so if it radiates, then it breaks the poison 995 00:42:25,442 --> 00:42:26,150 and the cat dies. 996 00:42:26,150 --> 00:42:28,280 If it doesn't radiate, then the cat survives. 997 00:42:28,280 --> 00:42:30,620 But until you observe it, it hasn't done either, 998 00:42:30,620 --> 00:42:33,507 so the cat's both alive and dead at the same time. 999 00:42:33,507 --> 00:42:35,840 JEFFREY GROSSMAN: And that was-- you see, that's exactly 1000 00:42:35,840 --> 00:42:38,310 right, very nice. 1001 00:42:38,310 --> 00:42:42,170 And the rest of that is you say, well-- 1002 00:42:42,170 --> 00:42:47,870 you put it so that it has a half life something like an hour, 1003 00:42:47,870 --> 00:42:51,690 roughly, between when it emits a particle. 1004 00:42:51,690 --> 00:42:54,350 And so then you measure it-- and so after an hour, 1005 00:42:54,350 --> 00:42:59,922 there's a 50-50 chance the cat has been killed or is alive. 1006 00:42:59,922 --> 00:43:01,880 But the key point is what you said there, which 1007 00:43:01,880 --> 00:43:05,750 is that, until you measure it-- 1008 00:43:05,750 --> 00:43:07,670 you see, the little radioactive thing 1009 00:43:07,670 --> 00:43:10,230 is a very quantum mechanical particle. 1010 00:43:10,230 --> 00:43:17,160 So until you measure it, as with the electron, it's everywhere. 1011 00:43:17,160 --> 00:43:21,600 It's both emitted and released the poison and not. 1012 00:43:21,600 --> 00:43:23,500 The state is quantum mechanical. 1013 00:43:23,500 --> 00:43:27,390 And so what Schrodinger did is he said, well, that's absurd. 1014 00:43:27,390 --> 00:43:31,590 Because then if you take that up to the macroscopic levels, 1015 00:43:31,590 --> 00:43:33,300 you can get these sort of absurdities. 1016 00:43:33,300 --> 00:43:34,860 And that's why he came up with this, 1017 00:43:34,860 --> 00:43:38,400 actually to make a point that we don't understand this yet. 1018 00:43:38,400 --> 00:43:39,990 That was really the point here. 1019 00:43:39,990 --> 00:43:42,100 And this paradox has been-- 1020 00:43:42,100 --> 00:43:43,950 and so, because the point being the cat 1021 00:43:43,950 --> 00:43:46,350 is both dead and alive according to quantum mechanics. 1022 00:43:46,350 --> 00:43:47,260 It is both. 1023 00:43:47,260 --> 00:43:50,910 It is a superposition of dead and alive 1024 00:43:50,910 --> 00:43:53,657 until you open the box, in which case, you collapse the wave 1025 00:43:53,657 --> 00:43:54,990 function because you observe it. 1026 00:43:58,290 --> 00:44:01,620 That would be really what quantum mechanics tells you. 1027 00:44:01,620 --> 00:44:08,370 And this paradox has been one of the central talking 1028 00:44:08,370 --> 00:44:10,200 points of quantum mechanics, or examples 1029 00:44:10,200 --> 00:44:15,780 used to illustrate how strange quantum mechanics is 1030 00:44:15,780 --> 00:44:16,543 for many decades. 1031 00:44:16,543 --> 00:44:18,210 And it's also led to a lot of discussion 1032 00:44:18,210 --> 00:44:21,780 on how we should actually interpret quantum mechanics. 1033 00:44:21,780 --> 00:44:24,473 This is called the Copenhagen interpretation, 1034 00:44:24,473 --> 00:44:26,640 for those of you who are interested in reading more, 1035 00:44:26,640 --> 00:44:27,840 but there are many, many others. 1036 00:44:27,840 --> 00:44:29,182 And I have a sheet at the end-- 1037 00:44:29,182 --> 00:44:30,390 I'm not going to go through-- 1038 00:44:30,390 --> 00:44:34,050 where I list like 10 or 15 different interpretations 1039 00:44:34,050 --> 00:44:35,280 of quantum mechanics. 1040 00:44:35,280 --> 00:44:36,480 How cool is that? 1041 00:44:36,480 --> 00:44:40,830 We really don't know what this all means. 1042 00:44:40,830 --> 00:44:42,270 And that's pretty neat. 1043 00:44:42,270 --> 00:44:45,555 Actually, Schrodinger, I think, he made this statement-- 1044 00:44:45,555 --> 00:44:46,680 which I thought was funny-- 1045 00:44:46,680 --> 00:44:47,557 about his paradox. 1046 00:44:47,557 --> 00:44:49,140 "I don't like it, and I'm sorry I ever 1047 00:44:49,140 --> 00:44:51,060 had anything to do with it." 1048 00:44:51,060 --> 00:44:53,940 Because I think it got taken out of context a lot as well, 1049 00:44:53,940 --> 00:44:57,060 and the whole killing cats is not a very PC-- 1050 00:44:57,060 --> 00:44:59,800 but he very carefully said, pardon my-- 1051 00:44:59,800 --> 00:45:02,970 in his paper, sorry for being so crude about talking 1052 00:45:02,970 --> 00:45:04,410 about dead cats. 1053 00:45:04,410 --> 00:45:07,100 And the final one to look into, but I won't talk about more, 1054 00:45:07,100 --> 00:45:09,210 is called the EPR paradox. 1055 00:45:09,210 --> 00:45:11,490 And this stands for Einstein, Podolsky, and Rosen. 1056 00:45:11,490 --> 00:45:14,270 And it's a very interesting paradox, again, 1057 00:45:14,270 --> 00:45:16,020 that comes out of quantum mechanics, which 1058 00:45:16,020 --> 00:45:22,630 is that you can entangle the states of two particles 1059 00:45:22,630 --> 00:45:23,710 together-- 1060 00:45:23,710 --> 00:45:27,100 let's say the spin-- so that its total is zero. 1061 00:45:27,100 --> 00:45:29,620 But one is one and one is minus one. 1062 00:45:29,620 --> 00:45:31,990 And now as you separate them, because they 1063 00:45:31,990 --> 00:45:34,750 were entangled at one point, you can separate them 1064 00:45:34,750 --> 00:45:38,140 to very long distances, and according to quantum mechanics, 1065 00:45:38,140 --> 00:45:40,420 they both have to really be both. 1066 00:45:40,420 --> 00:45:44,110 One cannot be one and one minus one-- the collection is zero. 1067 00:45:44,110 --> 00:45:46,540 But one cannot be one and one minus one until you measure 1068 00:45:46,540 --> 00:45:47,040 one. 1069 00:45:47,040 --> 00:45:49,180 And then that one is something, and the other one 1070 00:45:49,180 --> 00:45:51,100 is the other something. 1071 00:45:51,100 --> 00:45:53,740 And that actually leads to some very interesting paradoxes 1072 00:45:53,740 --> 00:45:56,290 involving information, because you've 1073 00:45:56,290 --> 00:45:58,570 gotten information about something that's more 1074 00:45:58,570 --> 00:46:01,480 than the speed of light away. 1075 00:46:01,480 --> 00:46:02,570 Is that possible? 1076 00:46:02,570 --> 00:46:04,450 [INAUDIBLE] wonderful discussions 1077 00:46:04,450 --> 00:46:07,900 about this kind of stuff that I won't go into. 1078 00:46:07,900 --> 00:46:08,500 OK. 1079 00:46:08,500 --> 00:46:11,470 So now we're going to get to-- 1080 00:46:11,470 --> 00:46:12,790 we're going to move-- 1081 00:46:12,790 --> 00:46:15,800 those are motivations. 1082 00:46:15,800 --> 00:46:18,670 This is what everybody was at the time grappling with, 1083 00:46:18,670 --> 00:46:22,380 is how can we explain these things? 1084 00:46:22,380 --> 00:46:25,660 And what it really came down to is that particles 1085 00:46:25,660 --> 00:46:27,760 can be both waves and-- 1086 00:46:27,760 --> 00:46:31,080 everything can be both waves and particles. 1087 00:46:31,080 --> 00:46:34,540 But especially when you get down to very small masses, 1088 00:46:34,540 --> 00:46:38,760 the wave nature can dominate. 1089 00:46:38,760 --> 00:46:41,610 And that is the case for electrons. 1090 00:46:41,610 --> 00:46:44,400 So for waves, they have particle-like properties, 1091 00:46:44,400 --> 00:46:46,985 and for particles, they can have wavelike properties. 1092 00:46:46,985 --> 00:46:49,680 And that's really the key observation. 1093 00:46:49,680 --> 00:46:51,810 That's the wave-particle duality. 1094 00:46:51,810 --> 00:46:57,420 And as you saw in the video, what that means is that-- 1095 00:46:57,420 --> 00:47:06,270 you see, a wave is a wave, which means it can have both-- 1096 00:47:06,270 --> 00:47:08,130 it can have interference. 1097 00:47:08,130 --> 00:47:11,400 As you saw, the electron, they shoot it one at a time. 1098 00:47:11,400 --> 00:47:13,020 Not interfering with another electron. 1099 00:47:13,020 --> 00:47:14,900 It's literally interfering with itself. 1100 00:47:17,218 --> 00:47:18,760 And you can see that you can actually 1101 00:47:18,760 --> 00:47:21,603 get interference patterns, and that diffraction pattern 1102 00:47:21,603 --> 00:47:23,770 that you see on the plate in the two-slit experiment 1103 00:47:23,770 --> 00:47:28,227 is a measurable wavelike property of the electron. 1104 00:47:28,227 --> 00:47:30,060 You know what I love so much about that is-- 1105 00:47:30,060 --> 00:47:32,070 I don't know if you caught it, but it's 1106 00:47:32,070 --> 00:47:34,670 shot out as a particle. 1107 00:47:34,670 --> 00:47:36,830 It's got to go through the slits as a wave. 1108 00:47:36,830 --> 00:47:39,660 There's no other way to explain it. 1109 00:47:39,660 --> 00:47:42,560 If you don't observe it, it goes through as a wave. 1110 00:47:42,560 --> 00:47:44,000 But then in order to-- 1111 00:47:44,000 --> 00:47:47,300 the original experiments were done with a photographic plate 1112 00:47:47,300 --> 00:47:49,310 that can only be-- 1113 00:47:49,310 --> 00:47:52,698 the track can only be made if it's a particle. 1114 00:47:52,698 --> 00:47:54,740 The position of the electron has to be a particle 1115 00:47:54,740 --> 00:47:56,630 to make the dot on the plate. 1116 00:47:56,630 --> 00:47:59,087 So it goes from particle to wave to particle. 1117 00:47:59,087 --> 00:48:01,170 And that's really the nature of quantum mechanics. 1118 00:48:01,170 --> 00:48:04,100 You have to be able to describe particles as waves. 1119 00:48:04,100 --> 00:48:06,710 And so we start seeing effects like this, 1120 00:48:06,710 --> 00:48:11,900 where you can get constructive interference from a particle. 1121 00:48:11,900 --> 00:48:13,820 That's really cool. 1122 00:48:13,820 --> 00:48:16,700 And that's what we need to be able to describe 1123 00:48:16,700 --> 00:48:20,220 to describe the quantum world in a computer. 1124 00:48:20,220 --> 00:48:20,850 That's real. 1125 00:48:20,850 --> 00:48:23,290 That's a water dropping to make waves. 1126 00:48:23,290 --> 00:48:25,650 This is actually an electron. 1127 00:48:25,650 --> 00:48:30,390 This is where an electron sits on a surface. 1128 00:48:30,390 --> 00:48:31,860 I think that's a quantum corral. 1129 00:48:35,040 --> 00:48:37,860 And it's been measured experimentally-- 1130 00:48:37,860 --> 00:48:40,740 this is the experimental setup. 1131 00:48:40,740 --> 00:48:42,410 It's been measured experimentally 1132 00:48:42,410 --> 00:48:44,610 for bigger things than electrons. 1133 00:48:44,610 --> 00:48:47,470 You think electrons are really tiny. 1134 00:48:47,470 --> 00:48:49,500 Oh, Grossman only cares about them 1135 00:48:49,500 --> 00:48:53,520 for his electronics and optics, but I care about bigger things, 1136 00:48:53,520 --> 00:48:54,480 like fullerenes. 1137 00:48:54,480 --> 00:48:58,590 Well, if you take fullerenes and you shoot them 1138 00:48:58,590 --> 00:49:03,750 through two slits, you also get a diffraction pattern. 1139 00:49:03,750 --> 00:49:04,750 This is real stuff. 1140 00:49:04,750 --> 00:49:07,830 It happens for real bigger things. 1141 00:49:07,830 --> 00:49:13,140 OK, but now, could I go through two slits? 1142 00:49:13,140 --> 00:49:14,070 Is that possible? 1143 00:49:14,070 --> 00:49:18,270 Am I quantum mechanical? 1144 00:49:18,270 --> 00:49:20,700 AUDIENCE: Are you observing yourself? 1145 00:49:20,700 --> 00:49:22,935 JEFFREY GROSSMAN: I am-- 1146 00:49:22,935 --> 00:49:23,435 I-- 1147 00:49:25,375 --> 00:49:27,660 I don't have a good response to that question. 1148 00:49:27,660 --> 00:49:31,440 But I am not observing myself and no one else is. 1149 00:49:31,440 --> 00:49:34,400 Am I quantum mechanical? 1150 00:49:34,400 --> 00:49:35,360 Yeah. 1151 00:49:35,360 --> 00:49:38,562 Why don't I create diffraction patterns wherever I go? 1152 00:49:38,562 --> 00:49:39,394 AUDIENCE: Too big. 1153 00:49:39,394 --> 00:49:40,680 JEFFREY GROSSMAN: Too big? 1154 00:49:40,680 --> 00:49:41,675 Don't read ahead! 1155 00:49:41,675 --> 00:49:42,930 Why am I too big? 1156 00:49:46,560 --> 00:49:49,510 So where does this stuff end? 1157 00:49:49,510 --> 00:49:53,577 Are you always a wave, no matter how big you are? 1158 00:49:53,577 --> 00:49:55,285 And that's where we're missing something. 1159 00:49:55,285 --> 00:49:56,890 We're missing something really important. 1160 00:49:56,890 --> 00:49:58,060 The answer is, absolutely. 1161 00:49:58,060 --> 00:50:01,990 I am a wave, and I'm proud of it. 1162 00:50:01,990 --> 00:50:06,140 My arm right now is a quantum mechanical-- this is a wave. 1163 00:50:06,140 --> 00:50:07,440 This is not a particle. 1164 00:50:07,440 --> 00:50:09,460 If I throw this chalk-- 1165 00:50:09,460 --> 00:50:12,850 that was fun-- that's not a particle. 1166 00:50:12,850 --> 00:50:15,250 That was a wave I just threw. 1167 00:50:15,250 --> 00:50:18,100 It has a wave associated with it. 1168 00:50:18,100 --> 00:50:19,420 It is very wavelike. 1169 00:50:19,420 --> 00:50:21,730 But if I throw chalk through two slits, 1170 00:50:21,730 --> 00:50:23,770 will I get a diffraction pattern? 1171 00:50:23,770 --> 00:50:25,130 No. 1172 00:50:25,130 --> 00:50:28,020 And now we're going to see why. 1173 00:50:28,020 --> 00:50:30,030 When is a particle like a wave? 1174 00:50:30,030 --> 00:50:32,220 Well, it always is-- 1175 00:50:32,220 --> 00:50:33,580 but to varying degrees. 1176 00:50:33,580 --> 00:50:37,290 And that's where de Broglie came in and generalized 1177 00:50:37,290 --> 00:50:41,190 what Einstein had been working on, and others, and said, look, 1178 00:50:41,190 --> 00:50:42,810 everything has a wave. 1179 00:50:42,810 --> 00:50:47,010 Everything is both a wave and a particle-- everything. 1180 00:50:47,010 --> 00:50:51,150 And he said, and we can associate-- 1181 00:50:51,150 --> 00:50:55,530 we can calculate a wavelength to these things. 1182 00:50:55,530 --> 00:50:56,630 Here's the electron. 1183 00:50:56,630 --> 00:51:01,710 The wavelength of the electron is 10 to the minus 10th meters. 1184 00:51:01,710 --> 00:51:06,990 Now, why is that a distance that is making electrons really 1185 00:51:06,990 --> 00:51:09,000 quantum mechanical? 1186 00:51:09,000 --> 00:51:14,310 Or why can't I describe them classically at that distance? 1187 00:51:14,310 --> 00:51:16,170 What's that distance? 1188 00:51:16,170 --> 00:51:17,160 AUDIENCE: Angstrom? 1189 00:51:17,160 --> 00:51:19,140 JEFFREY GROSSMAN: It's an angstrom. 1190 00:51:19,140 --> 00:51:23,000 What happens at the angstrom level? 1191 00:51:23,000 --> 00:51:24,140 Like, what's an angstrom? 1192 00:51:24,140 --> 00:51:26,270 What's 4 angstroms? 1193 00:51:26,270 --> 00:51:28,232 What's 2.447 angstroms? 1194 00:51:28,232 --> 00:51:28,940 AUDIENCE: Carbon. 1195 00:51:28,940 --> 00:51:30,430 JEFFREY GROSSMAN: Carbon. 1196 00:51:30,430 --> 00:51:31,510 Yeah, [INAUDIBLE] carbon. 1197 00:51:34,490 --> 00:51:36,390 So that's the level of bonds. 1198 00:51:36,390 --> 00:51:37,810 This is it, man. 1199 00:51:37,810 --> 00:51:41,440 This is where-- that wavelength is 1200 00:51:41,440 --> 00:51:44,650 the same size as the kind of distances 1201 00:51:44,650 --> 00:51:47,440 that matter to an electron, like the distance from one 1202 00:51:47,440 --> 00:51:48,970 atom to another. 1203 00:51:48,970 --> 00:51:50,240 It's the same. 1204 00:51:50,240 --> 00:51:51,970 So that means-- because the wavelength 1205 00:51:51,970 --> 00:51:57,110 is so similar to the world of the electron, 1206 00:51:57,110 --> 00:52:01,403 then that quantum effect is going to be really important. 1207 00:52:01,403 --> 00:52:04,640 And the wavelength is 100 times smaller 1208 00:52:04,640 --> 00:52:08,060 for a fullerene, which means that it's maybe 1209 00:52:08,060 --> 00:52:11,480 less important for things we do with fullerenes. 1210 00:52:11,480 --> 00:52:14,300 What do we do with fullerenes, by the way? 1211 00:52:14,300 --> 00:52:17,930 Has anybody done anything with fullerenes? 1212 00:52:17,930 --> 00:52:20,513 Probably not, but what could we do with fullerenes? 1213 00:52:23,900 --> 00:52:24,770 No. 1214 00:52:24,770 --> 00:52:26,150 We're still working on it. 1215 00:52:26,150 --> 00:52:26,660 Make what? 1216 00:52:26,660 --> 00:52:27,710 AUDIENCE: Make soccer balls. 1217 00:52:27,710 --> 00:52:29,002 JEFFREY GROSSMAN: Soccer balls. 1218 00:52:31,250 --> 00:52:33,920 You can make pretty high temperature superconductors-- 1219 00:52:33,920 --> 00:52:36,140 what would have been considered very high temperature 1220 00:52:36,140 --> 00:52:38,300 before high TC came on. 1221 00:52:38,300 --> 00:52:40,370 You can also make solar cells. 1222 00:52:40,370 --> 00:52:41,450 You can make electronics. 1223 00:52:41,450 --> 00:52:44,535 You can make all kinds of interesting chemistries. 1224 00:52:44,535 --> 00:52:46,910 And most of the time, the quantum mechanics won't matter, 1225 00:52:46,910 --> 00:52:49,290 but that experiment showed that you can still measure it. 1226 00:52:49,290 --> 00:52:51,770 Now I have a baseball, and here's 1227 00:52:51,770 --> 00:52:54,080 the wavelength of a baseball. 1228 00:52:54,080 --> 00:52:57,230 Can I measure that? 1229 00:52:57,230 --> 00:53:00,250 But it has a wavelength. 1230 00:53:00,250 --> 00:53:03,520 And it's just-- and so do I. So do you. 1231 00:53:03,520 --> 00:53:05,860 It's just that this is 20 orders of magnitude 1232 00:53:05,860 --> 00:53:09,780 smaller than the diameter of the nucleus of an atom. 1233 00:53:09,780 --> 00:53:12,810 That's how tiny the wavelength is associated 1234 00:53:12,810 --> 00:53:15,150 with these more larger objects. 1235 00:53:15,150 --> 00:53:17,700 So you see, these are very quantum mechanical, 1236 00:53:17,700 --> 00:53:19,410 and they do have-- 1237 00:53:19,410 --> 00:53:23,140 they would be able to give you the same effect, 1238 00:53:23,140 --> 00:53:25,540 if you could pick up-- 1239 00:53:25,540 --> 00:53:27,370 if you can measure distances that small. 1240 00:53:31,970 --> 00:53:38,710 So what we have in classical versus quantum 1241 00:53:38,710 --> 00:53:42,280 is that we have to describe in a computer 1242 00:53:42,280 --> 00:53:44,800 the mechanics of waves, as opposed 1243 00:53:44,800 --> 00:53:46,340 to the mechanics of particles. 1244 00:53:46,340 --> 00:53:47,343 So what we had before-- 1245 00:53:47,343 --> 00:53:48,760 OK, so that way, we're going to be 1246 00:53:48,760 --> 00:53:52,300 able to describe the wave and the particle behavior. 1247 00:53:52,300 --> 00:53:55,470 What we had before was this. 1248 00:53:55,470 --> 00:53:57,310 This is the mechanics of a particle, 1249 00:53:57,310 --> 00:54:00,130 and you all did a lot of simulating of this. 1250 00:54:02,820 --> 00:54:04,410 Did you guys do-- 1251 00:54:04,410 --> 00:54:07,890 so did you do molecular dynamics? 1252 00:54:07,890 --> 00:54:08,420 Yeah. 1253 00:54:08,420 --> 00:54:10,010 So you know about that. 1254 00:54:10,010 --> 00:54:14,160 And you did that with velocity [INAUDIBLE],, leapfrog. 1255 00:54:18,480 --> 00:54:20,460 No? 1256 00:54:20,460 --> 00:54:23,250 How did you integrate that? 1257 00:54:23,250 --> 00:54:25,350 Did you pick an integration scheme? 1258 00:54:25,350 --> 00:54:28,350 How did you solve that equation? 1259 00:54:28,350 --> 00:54:29,780 You clicked Simulate. 1260 00:54:31,540 --> 00:54:32,770 But there are probably-- 1261 00:54:32,770 --> 00:54:33,950 yeah, go ahead. 1262 00:54:33,950 --> 00:54:38,760 AUDIENCE: He showed us one scheme where we used, I think, 1263 00:54:38,760 --> 00:54:42,450 the two subsequent positions sort of got an average velocity 1264 00:54:42,450 --> 00:54:44,770 out of that, and-- 1265 00:54:44,770 --> 00:54:45,850 JEFFREY GROSSMAN: Great. 1266 00:54:45,850 --> 00:54:46,460 AUDIENCE: Got it from there. 1267 00:54:46,460 --> 00:54:47,050 JEFFREY GROSSMAN: Yeah. 1268 00:54:47,050 --> 00:54:48,240 And so they're-- right. 1269 00:54:48,240 --> 00:54:49,460 So here's the thing. 1270 00:54:49,460 --> 00:54:52,630 There are many ways to solve this equation. 1271 00:54:52,630 --> 00:54:57,910 And some are more efficient to put on a computer than others. 1272 00:54:57,910 --> 00:55:01,190 But none of them are really very complicated. 1273 00:55:01,190 --> 00:55:03,640 We're going to have the same thing with quantum mechanics, 1274 00:55:03,640 --> 00:55:05,265 it just gets a little more complicated, 1275 00:55:05,265 --> 00:55:07,385 because the equation is more complicated. 1276 00:55:07,385 --> 00:55:09,010 But we're going to have the same thing. 1277 00:55:09,010 --> 00:55:10,630 We'll have an equation for quantum mechanics, 1278 00:55:10,630 --> 00:55:12,213 and there'll be many ways to solve it. 1279 00:55:12,213 --> 00:55:15,400 And we're going to learn a little bit about them, 1280 00:55:15,400 --> 00:55:17,302 and then just kind of move on and apply it. 1281 00:55:17,302 --> 00:55:19,510 But we'll learn a little bit about the different ways 1282 00:55:19,510 --> 00:55:21,830 to solve it. 1283 00:55:21,830 --> 00:55:26,130 So this wave is now-- you see, instead of being a particle, 1284 00:55:26,130 --> 00:55:27,540 it's now an expectation. 1285 00:55:27,540 --> 00:55:28,430 It's a vibration. 1286 00:55:28,430 --> 00:55:30,600 So what we need to know about a wave-- 1287 00:55:30,600 --> 00:55:33,780 oh, yeah, psi. 1288 00:55:33,780 --> 00:55:35,040 Psi. 1289 00:55:35,040 --> 00:55:38,870 When you see psi, that's like quantum mechanics, right? 1290 00:55:38,870 --> 00:55:39,870 Or a fraternity? 1291 00:55:39,870 --> 00:55:41,830 I don't know. 1292 00:55:41,830 --> 00:55:43,710 But anyway, here it's quantum mechanics. 1293 00:55:43,710 --> 00:55:45,720 And psi is the function. 1294 00:55:45,720 --> 00:55:46,238 That's it. 1295 00:55:46,238 --> 00:55:47,405 That's what we want to know. 1296 00:55:47,405 --> 00:55:50,520 That's the wave function. 1297 00:55:50,520 --> 00:55:55,240 That's what we're solving for for the next so many weeks-- 1298 00:55:55,240 --> 00:55:56,020 five weeks? 1299 00:55:56,020 --> 00:55:58,632 Six weeks. 1300 00:55:58,632 --> 00:56:00,090 We're going to be solving for this. 1301 00:56:00,090 --> 00:56:01,230 This is the wave function. 1302 00:56:01,230 --> 00:56:05,490 This is what tells us where those electrons are going to be 1303 00:56:05,490 --> 00:56:07,270 and how they're going to behave. 1304 00:56:07,270 --> 00:56:09,360 And so the simplest way to write down a wave 1305 00:56:09,360 --> 00:56:12,270 is what's called the plane wave, which is just a cosine-- 1306 00:56:12,270 --> 00:56:16,560 it's a cosine plus sine, where you have an amplitude, 1307 00:56:16,560 --> 00:56:22,980 and then you have this vector k at the spatial position, 1308 00:56:22,980 --> 00:56:25,947 and then this frequency times the time. 1309 00:56:25,947 --> 00:56:27,780 So this is the simplest way to write a wave, 1310 00:56:27,780 --> 00:56:29,790 and you can find little nice animations 1311 00:56:29,790 --> 00:56:34,430 on Wikipedia of what a wave like that would look like. 1312 00:56:34,430 --> 00:56:36,740 That's a plane wave. 1313 00:56:36,740 --> 00:56:39,350 And you can see that it's called a plane wave because you 1314 00:56:39,350 --> 00:56:43,220 can look at it as these moving planes of some sort 1315 00:56:43,220 --> 00:56:45,770 of constant magnitude. 1316 00:56:45,770 --> 00:56:49,842 It's a very simple way of describing this. 1317 00:56:49,842 --> 00:56:51,340 Maybe there are more complex ways, 1318 00:56:51,340 --> 00:56:55,300 but this is going to be one that we like in this class. 1319 00:56:55,300 --> 00:56:58,280 Now, what I was telling you about before is 1320 00:56:58,280 --> 00:57:00,320 what de Broglie did, which he said, look, 1321 00:57:00,320 --> 00:57:04,490 everything can be described as a wave. 1322 00:57:04,490 --> 00:57:06,830 Everything can have a wavelength. 1323 00:57:06,830 --> 00:57:09,920 And the wavelength associated with anything 1324 00:57:09,920 --> 00:57:11,840 is going to look like this. 1325 00:57:11,840 --> 00:57:12,590 Did I put it here? 1326 00:57:12,590 --> 00:57:13,220 Yeah. 1327 00:57:13,220 --> 00:57:17,390 It's going to go as h divided by the momentum-- 1328 00:57:17,390 --> 00:57:21,190 the mass times the velocity. 1329 00:57:21,190 --> 00:57:22,660 So there is a wavelength that can 1330 00:57:22,660 --> 00:57:25,360 be associated with anything. 1331 00:57:25,360 --> 00:57:26,890 That's what de Broglie said. 1332 00:57:26,890 --> 00:57:30,880 So he generalized what Einstein had been working on 1333 00:57:30,880 --> 00:57:34,630 with light to say that this would be something 1334 00:57:34,630 --> 00:57:35,590 that anything can have. 1335 00:57:35,590 --> 00:57:39,550 It can have a description that can be 1336 00:57:39,550 --> 00:57:43,340 described by a wave function. 1337 00:57:43,340 --> 00:57:45,890 And that's what Einstein already did this. 1338 00:57:45,890 --> 00:57:46,640 He did that part. 1339 00:57:46,640 --> 00:57:49,160 He said the energy of that wave would be 1340 00:57:49,160 --> 00:57:50,750 proportional to its frequency. 1341 00:57:50,750 --> 00:57:53,610 That was part of the photoelectric effect. 1342 00:57:53,610 --> 00:57:55,560 OK, so how do we describe it? 1343 00:57:55,560 --> 00:58:01,140 So in the last 10, 15 minutes, we'll say, this is it. 1344 00:58:01,140 --> 00:58:03,300 This is where we've been building to, 1345 00:58:03,300 --> 00:58:05,070 because we're going to end with what 1346 00:58:05,070 --> 00:58:08,070 we need to do in this class, which is solve an equation. 1347 00:58:08,070 --> 00:58:10,500 We're going to end just with a little bit of feeling 1348 00:58:10,500 --> 00:58:13,080 of our F equals ma. 1349 00:58:13,080 --> 00:58:16,260 And our F equals ma is the Schrodinger equation. 1350 00:58:16,260 --> 00:58:20,970 And I won't talk about how it was derived. 1351 00:58:23,680 --> 00:58:25,890 It's actually-- it's a wonderful story. 1352 00:58:25,890 --> 00:58:28,780 He was very frustrated, because this didn't actually 1353 00:58:28,780 --> 00:58:30,340 agree with some of the work that was 1354 00:58:30,340 --> 00:58:33,860 being done on relativistic effects solving this equation. 1355 00:58:33,860 --> 00:58:36,710 And so he refused to publish, actually, 1356 00:58:36,710 --> 00:58:38,590 his equation for quite a time. 1357 00:58:38,590 --> 00:58:41,170 And he took a retreat to his cabin, 1358 00:58:41,170 --> 00:58:45,880 and apparently came back and decided he would publish. 1359 00:58:45,880 --> 00:58:48,340 I love reading these stories. 1360 00:58:48,340 --> 00:58:49,210 Those were the days. 1361 00:58:49,210 --> 00:58:51,070 People really published when they really 1362 00:58:51,070 --> 00:58:53,770 had something important to say. 1363 00:58:53,770 --> 00:58:56,560 That's cool. 1364 00:58:56,560 --> 00:58:57,940 And that was-- it was just really 1365 00:58:57,940 --> 00:59:00,460 neat to watch the communication between Schrodinger 1366 00:59:00,460 --> 00:59:06,550 and Einstein, and all these just brilliant people of the time. 1367 00:59:06,550 --> 00:59:07,450 This is our equation. 1368 00:59:07,450 --> 00:59:10,708 This is a wave equation. 1369 00:59:10,708 --> 00:59:12,850 This tells us what we need to know. 1370 00:59:12,850 --> 00:59:18,220 This tells us how this function evolved in time and space. 1371 00:59:18,220 --> 00:59:26,230 And the key here is that this side here has the terms-- 1372 00:59:26,230 --> 00:59:31,240 this has the momentum squared term, which-- you 1373 00:59:31,240 --> 00:59:33,040 can look at the previous page. 1374 00:59:33,040 --> 00:59:37,460 When you look at de Broglie and Einstein, 1375 00:59:37,460 --> 00:59:41,890 h bar omega is the energy from the frequency, 1376 00:59:41,890 --> 00:59:43,660 and then the momentum, then you can 1377 00:59:43,660 --> 00:59:47,590 go back and see why these things make a lot of sense. 1378 00:59:47,590 --> 00:59:50,470 But this is going to be-- 1379 00:59:50,470 --> 00:59:53,350 this second derivative here, spatial derivative, 1380 00:59:53,350 --> 00:59:56,420 is going to give you the momentum squared. 1381 00:59:56,420 --> 00:59:59,360 So that looks kind of like a kinetic energy term. 1382 00:59:59,360 --> 01:00:03,020 And that's the kinetic energy plus the potential energy 1383 01:00:03,020 --> 01:00:07,400 times the wave function gives you 1384 01:00:07,400 --> 01:00:11,060 something that's equal to the time dependence of that wave 1385 01:00:11,060 --> 01:00:11,885 function. 1386 01:00:11,885 --> 01:00:14,120 The time derivative of the wave function. 1387 01:00:14,120 --> 01:00:15,770 That's the Schrodinger equation. 1388 01:00:15,770 --> 01:00:24,650 And for this class, we will consider that left-hand part 1389 01:00:24,650 --> 01:00:30,340 that has the parts that give you the potential energy 1390 01:00:30,340 --> 01:00:31,390 and the kinetic energy. 1391 01:00:31,390 --> 01:00:35,660 That's basically how you can think of this, of the particle. 1392 01:00:35,660 --> 01:00:38,600 But oh, that's the kinetic energy of the particle, 1393 01:00:38,600 --> 01:00:41,520 but for a wave. 1394 01:00:41,520 --> 01:00:43,200 And again, you can see why, because you 1395 01:00:43,200 --> 01:00:45,660 can go back and see what this gives you, 1396 01:00:45,660 --> 01:00:48,150 what k this gives you. 1397 01:00:48,150 --> 01:00:54,150 So that's the kinetic energy, but it's meant for a wave. 1398 01:00:54,150 --> 01:00:57,360 And if we assume that this energy part doesn't depend 1399 01:00:57,360 --> 01:00:58,950 on time, then the Schrodinger equation 1400 01:00:58,950 --> 01:01:01,200 is much easier to solve, and we get something 1401 01:01:01,200 --> 01:01:02,300 that's time-independent. 1402 01:01:02,300 --> 01:01:03,925 And that's what we'll do in this class, 1403 01:01:03,925 --> 01:01:07,130 because we can separate it into a spatial part and a time part, 1404 01:01:07,130 --> 01:01:08,880 and then we can just ignore the time part, 1405 01:01:08,880 --> 01:01:12,780 and we can call both sides equal to a constant. 1406 01:01:12,780 --> 01:01:15,460 This is just some very simple algebra. 1407 01:01:15,460 --> 01:01:17,340 And if we do that, we can set them both equal 1408 01:01:17,340 --> 01:01:20,220 to some constant, let's call it E, which is-- 1409 01:01:20,220 --> 01:01:22,120 there's a reason for that. 1410 01:01:22,120 --> 01:01:24,330 And then this full psi with the time 1411 01:01:24,330 --> 01:01:27,240 will depend on the spatial part times this exponential, 1412 01:01:27,240 --> 01:01:29,162 and we'll just ignore this for this class. 1413 01:01:29,162 --> 01:01:30,870 We're just going to care about this part. 1414 01:01:34,440 --> 01:01:36,030 OK. 1415 01:01:36,030 --> 01:01:38,625 So let's end with-- there's these couple of examples 1416 01:01:38,625 --> 01:01:39,750 that some of you have seen. 1417 01:01:39,750 --> 01:01:41,750 How many of you have not seen particle in a box? 1418 01:01:44,390 --> 01:01:45,300 Couple people. 1419 01:01:45,300 --> 01:01:46,320 OK. 1420 01:01:46,320 --> 01:01:47,790 But if you have seen it, you know 1421 01:01:47,790 --> 01:01:50,580 this is still going to be fun, because particle in a box 1422 01:01:50,580 --> 01:01:52,510 is always fun. 1423 01:01:52,510 --> 01:01:58,230 So all particle in a box is it's the spatial part 1424 01:01:58,230 --> 01:02:04,500 of the Schrodinger equation solved for one of the simplest 1425 01:02:04,500 --> 01:02:06,480 systems you can imagine, which is 1426 01:02:06,480 --> 01:02:10,780 that you have some quantum mechanical particle that can 1427 01:02:10,780 --> 01:02:13,690 exist inside of this region. 1428 01:02:13,690 --> 01:02:16,400 And so in this region, there's no potential energy. 1429 01:02:16,400 --> 01:02:18,880 It's just a free particle. 1430 01:02:18,880 --> 01:02:21,100 It's a free wave. 1431 01:02:21,100 --> 01:02:25,060 But then it has these boundaries that go to infinity. 1432 01:02:25,060 --> 01:02:26,650 And because it has a potential that's 1433 01:02:26,650 --> 01:02:30,300 infinite at the boundaries there's 1434 01:02:30,300 --> 01:02:34,540 only one solution here, which is that the function has 1435 01:02:34,540 --> 01:02:36,160 to be zero. 1436 01:02:36,160 --> 01:02:40,790 And you can convince yourself of that just by looking at this. 1437 01:02:40,790 --> 01:02:44,432 If this is infinity, psi has to be zero. 1438 01:02:44,432 --> 01:02:45,390 It's the only solution. 1439 01:02:48,210 --> 01:02:50,910 So here's what becomes really interesting about this. 1440 01:02:50,910 --> 01:02:54,160 So you have-- if you look at this equation, and you say, 1441 01:02:54,160 --> 01:02:56,820 well, OK, outside-- 1442 01:02:56,820 --> 01:02:59,100 so you have two equations you can write-- one 1443 01:02:59,100 --> 01:03:00,960 where there's a V, but it's infinite, 1444 01:03:00,960 --> 01:03:04,380 in this case, and one where V is zero, in which case 1445 01:03:04,380 --> 01:03:07,150 that part drops out, and this is the equation you're solving. 1446 01:03:07,150 --> 01:03:10,010 And this has a general solution, which looks like this. 1447 01:03:10,010 --> 01:03:13,570 It's a sine plus a cosine. 1448 01:03:13,570 --> 01:03:16,120 And from this general solution, you 1449 01:03:16,120 --> 01:03:19,030 can actually write down what E is. 1450 01:03:19,030 --> 01:03:22,810 That's actually very fairly simple algebra to get to that. 1451 01:03:22,810 --> 01:03:26,350 But what becomes really interesting and exciting 1452 01:03:26,350 --> 01:03:28,340 is when you apply the boundary conditions. 1453 01:03:28,340 --> 01:03:30,970 So when you look at what has to happen here, 1454 01:03:30,970 --> 01:03:33,760 you have constraints. 1455 01:03:33,760 --> 01:03:37,010 And those constraints lead to something really important 1456 01:03:37,010 --> 01:03:40,520 that was really, really frustrating all these people. 1457 01:03:40,520 --> 01:03:42,212 What is it? 1458 01:03:42,212 --> 01:03:43,170 AUDIENCE: Quantization. 1459 01:03:43,170 --> 01:03:44,940 JEFFREY GROSSMAN: Leads to quantization. 1460 01:03:44,940 --> 01:03:45,810 That's it. 1461 01:03:45,810 --> 01:03:47,130 That's the ticket. 1462 01:03:47,130 --> 01:03:51,630 It's when you put boundary conditions on the simplest 1463 01:03:51,630 --> 01:03:57,170 quantum particle, quantum thing imaginable, a thing in a box, 1464 01:03:57,170 --> 01:03:59,150 you quantize it. 1465 01:03:59,150 --> 01:04:01,550 You quantize it because, you see, 1466 01:04:01,550 --> 01:04:03,800 when I put these boundary conditions on, 1467 01:04:03,800 --> 01:04:08,630 I'm saying that there are only certain allowable values 1468 01:04:08,630 --> 01:04:13,520 for this, because of this. 1469 01:04:18,130 --> 01:04:20,440 So the boundary conditions cause quantization, 1470 01:04:20,440 --> 01:04:23,110 and that's what gives rise to the whole thing. 1471 01:04:23,110 --> 01:04:29,230 That's what gives rise to this whole world of energy levels, 1472 01:04:29,230 --> 01:04:30,940 and a lot of the things that we talked 1473 01:04:30,940 --> 01:04:35,870 about in the beginning that were so challenging to understand. 1474 01:04:35,870 --> 01:04:36,950 So you have quantization. 1475 01:04:36,950 --> 01:04:38,117 You also have normalization. 1476 01:04:38,117 --> 01:04:41,120 We're not going to go through this in great detail, 1477 01:04:41,120 --> 01:04:45,560 but that also helps you understand what A is. 1478 01:04:45,560 --> 01:04:47,825 But you see there, that has to be. 1479 01:04:47,825 --> 01:04:52,820 k can only be n pi over L where n is some integer. 1480 01:04:52,820 --> 01:04:56,360 It can only be that because of those boundaries. 1481 01:04:56,360 --> 01:04:59,630 And if you go back to the previous page, you can see why. 1482 01:04:59,630 --> 01:05:03,320 So now, your energy, which was nice and general as k, 1483 01:05:03,320 --> 01:05:06,500 going as k squared, can only go as n squared 1484 01:05:06,500 --> 01:05:07,650 h bar squared pi squared. 1485 01:05:07,650 --> 01:05:11,360 So it can only go at certain values. 1486 01:05:11,360 --> 01:05:12,710 It cannot be anything else. 1487 01:05:15,900 --> 01:05:18,480 And what you get, then, is you get energies. 1488 01:05:18,480 --> 01:05:22,830 So you get energies that have very discrete values. 1489 01:05:22,830 --> 01:05:25,050 And that starts to remind me of what? 1490 01:05:25,050 --> 01:05:27,722 What experiment? 1491 01:05:27,722 --> 01:05:28,722 AUDIENCE: Photoelectric? 1492 01:05:28,722 --> 01:05:30,055 JEFFREY GROSSMAN: Photoelectric? 1493 01:05:30,055 --> 01:05:31,430 OK. 1494 01:05:31,430 --> 01:05:34,902 And what else, where you only saw discrete values? 1495 01:05:34,902 --> 01:05:35,860 AUDIENCE: The spectrum? 1496 01:05:35,860 --> 01:05:37,760 JEFFREY GROSSMAN: The spectra. 1497 01:05:37,760 --> 01:05:38,960 The lines. 1498 01:05:38,960 --> 01:05:40,992 You only saw discrete colors. 1499 01:05:40,992 --> 01:05:42,200 You only see discrete colors. 1500 01:05:42,200 --> 01:05:45,350 You guys can take a telescope and look, 1501 01:05:45,350 --> 01:05:46,880 and you'll only see discrete colors. 1502 01:05:46,880 --> 01:05:48,950 Now, it also gives you something else. 1503 01:05:48,950 --> 01:05:52,970 It gives you psi, which gives you these curves. 1504 01:05:52,970 --> 01:05:58,620 So you see, for the first solution, n equals 1, 1505 01:05:58,620 --> 01:06:00,580 you get a psi that looks like that. 1506 01:06:00,580 --> 01:06:02,760 But for the next allowed value, you 1507 01:06:02,760 --> 01:06:04,200 get a different shape for psi. 1508 01:06:04,200 --> 01:06:05,790 And for the next allowed value, you 1509 01:06:05,790 --> 01:06:08,840 get yet another shape for psi. 1510 01:06:08,840 --> 01:06:11,060 Oh, boy, is this important. 1511 01:06:11,060 --> 01:06:12,170 Seriously. 1512 01:06:12,170 --> 01:06:13,430 Check this out, OK? 1513 01:06:13,430 --> 01:06:16,310 Because now-- OK, so that helps explain this. 1514 01:06:16,310 --> 01:06:18,140 It looks like it might. 1515 01:06:18,140 --> 01:06:24,200 And now we're going to do it for V equals something that 1516 01:06:24,200 --> 01:06:27,710 looks more like a harmonic potential, 1517 01:06:27,710 --> 01:06:31,710 and we're going to get equations that look like this. 1518 01:06:31,710 --> 01:06:32,210 You see? 1519 01:06:32,210 --> 01:06:33,710 We get energy levels-- 1520 01:06:33,710 --> 01:06:35,930 the quantized energy levels that look like this, 1521 01:06:35,930 --> 01:06:38,217 and we get psis that look like this. 1522 01:06:38,217 --> 01:06:40,550 And these are psi squareds, which I'll tell you about in 1523 01:06:40,550 --> 01:06:42,680 a minute. 1524 01:06:42,680 --> 01:06:46,190 And that starts to look a whole lot-- 1525 01:06:46,190 --> 01:06:47,150 do I have it? 1526 01:06:47,150 --> 01:06:52,880 That starts to look a whole lot like the hydrogen atom. 1527 01:06:52,880 --> 01:06:55,880 You see, look at these psis. 1528 01:06:55,880 --> 01:06:58,840 Look at the shapes of those. 1529 01:06:58,840 --> 01:07:01,080 Those have structure, and they also have zeros. 1530 01:07:01,080 --> 01:07:03,770 They have places where they go to zero. 1531 01:07:03,770 --> 01:07:05,900 Now, here's the critical thing. 1532 01:07:05,900 --> 01:07:11,850 The shape of the psi squared is the answer. 1533 01:07:11,850 --> 01:07:15,090 It's where the electron is going to be. 1534 01:07:15,090 --> 01:07:20,800 It is the probability of finding the electron anywhere in space. 1535 01:07:20,800 --> 01:07:22,630 Psi squared is the probability of finding 1536 01:07:22,630 --> 01:07:26,310 a quantum mechanical particle anywhere in space. 1537 01:07:26,310 --> 01:07:28,930 It is the wave function, and it is also 1538 01:07:28,930 --> 01:07:31,720 where the particle will be with a given probability. 1539 01:07:31,720 --> 01:07:36,640 So the probability of finding this particle in a harmonic 1540 01:07:36,640 --> 01:07:39,490 well is going to be largest here, 1541 01:07:39,490 --> 01:07:41,980 and then almost zero there. 1542 01:07:41,980 --> 01:07:45,740 And then it's going to go up again, further out. 1543 01:07:45,740 --> 01:07:47,410 And you have these different solutions 1544 01:07:47,410 --> 01:07:51,100 that only happen for certain energies. 1545 01:07:51,100 --> 01:07:53,860 That is exactly what's observed. 1546 01:07:53,860 --> 01:07:57,220 So the psi squared is the probability 1547 01:07:57,220 --> 01:07:58,270 you find a particle. 1548 01:08:01,370 --> 01:08:04,310 Psi, we don't know what it is. 1549 01:08:04,310 --> 01:08:06,280 We don't know what psi is. 1550 01:08:06,280 --> 01:08:07,910 Does anybody know what psi is? 1551 01:08:07,910 --> 01:08:09,200 AUDIENCE: [INAUDIBLE] 1552 01:08:09,200 --> 01:08:12,782 JEFFREY GROSSMAN: No, that's psi squared. 1553 01:08:12,782 --> 01:08:14,990 Psi is what we solve for in the Schrodinger equation, 1554 01:08:14,990 --> 01:08:17,073 and that's we're going to solve for in this class. 1555 01:08:17,073 --> 01:08:19,220 Psi squared gives us the probability 1556 01:08:19,220 --> 01:08:21,260 of finding that particle. 1557 01:08:21,260 --> 01:08:21,979 What is psi? 1558 01:08:30,170 --> 01:08:30,920 What does it mean? 1559 01:08:33,750 --> 01:08:34,274 Any guesses? 1560 01:08:38,439 --> 01:08:40,899 The square of it is the probability 1561 01:08:40,899 --> 01:08:43,279 that you can find a particle anywhere. 1562 01:08:43,279 --> 01:08:46,270 But what is psi itself? 1563 01:08:46,270 --> 01:08:50,890 People have struggled with this a lot. 1564 01:08:50,890 --> 01:08:52,120 And you know what I think? 1565 01:08:52,120 --> 01:08:54,220 I think people have given up. 1566 01:08:54,220 --> 01:08:56,140 Because when you read old textbooks, 1567 01:08:56,140 --> 01:08:57,260 old quantum textbooks-- 1568 01:08:57,260 --> 01:09:00,189 I'm talking from the '30s and '40s, 1569 01:09:00,189 --> 01:09:01,880 they talk about that a whole lot. 1570 01:09:01,880 --> 01:09:03,640 And when you read new quantum textbooks, 1571 01:09:03,640 --> 01:09:06,359 they don't talk about it anymore. 1572 01:09:06,359 --> 01:09:08,040 Because we just don't really know, 1573 01:09:08,040 --> 01:09:11,160 is the answer, what is the physical meaning of psi. 1574 01:09:11,160 --> 01:09:13,520 Isn't that so cool? 1575 01:09:13,520 --> 01:09:17,297 We don't really have a good grip on it. 1576 01:09:17,297 --> 01:09:18,880 There's a lot of different discussions 1577 01:09:18,880 --> 01:09:20,529 around what it could be. 1578 01:09:20,529 --> 01:09:22,279 But this is the thing that means something 1579 01:09:22,279 --> 01:09:23,810 we can measure directly. 1580 01:09:23,810 --> 01:09:27,590 It's the distribution of where that particle is. 1581 01:09:27,590 --> 01:09:29,569 You see, so this is it. 1582 01:09:29,569 --> 01:09:31,250 This is an electron around-- 1583 01:09:31,250 --> 01:09:34,790 this is the electron of hydrogen. And you see, 1584 01:09:34,790 --> 01:09:38,150 when that electron is in-- let's take a look at this. 1585 01:09:38,150 --> 01:09:40,609 This is really important. 1586 01:09:43,540 --> 01:09:46,990 When that electron is in this shell, 1587 01:09:46,990 --> 01:09:50,395 we already know that's called the 1s. 1588 01:09:50,395 --> 01:09:53,670 The psi for that first allowed energy 1589 01:09:53,670 --> 01:09:58,090 level, that first allowed energy level has a shape to it, 1590 01:09:58,090 --> 01:10:00,290 and it's spherical, and it looks like that. 1591 01:10:00,290 --> 01:10:04,420 And therefore, that is the probability distribution 1592 01:10:04,420 --> 01:10:05,120 of the electron. 1593 01:10:05,120 --> 01:10:06,790 That's where it can be in space. 1594 01:10:09,805 --> 01:10:16,550 If I measure where that electron is, where's it going to be? 1595 01:10:23,140 --> 01:10:24,430 Yeah. 1596 01:10:24,430 --> 01:10:26,260 AUDIENCE: I mean, if you measure it, 1597 01:10:26,260 --> 01:10:28,720 you're going to get back some position for it, 1598 01:10:28,720 --> 01:10:30,850 and it's going to be at that position. 1599 01:10:30,850 --> 01:10:32,410 JEFFREY GROSSMAN: And I love that. 1600 01:10:32,410 --> 01:10:35,080 If I measure it, it will be where I measure it. 1601 01:10:35,080 --> 01:10:35,878 Which is true. 1602 01:10:35,878 --> 01:10:37,420 And that's actually the right answer. 1603 01:10:37,420 --> 01:10:40,120 But where will it be according to that picture? 1604 01:10:40,120 --> 01:10:43,300 How can I use this picture to tell me where it's going to be? 1605 01:10:48,750 --> 01:10:52,820 That is psi squared for the electron of hydrogen 1606 01:10:52,820 --> 01:10:53,690 in the first level. 1607 01:10:59,040 --> 01:10:59,540 Yeah. 1608 01:10:59,633 --> 01:11:01,050 AUDIENCE: You guess as to where it 1609 01:11:01,050 --> 01:11:04,252 will be within that boundary. 1610 01:11:04,252 --> 01:11:05,210 JEFFREY GROSSMAN: Yeah. 1611 01:11:05,210 --> 01:11:09,200 I mean, basically, the answer is that it tells me 1612 01:11:09,200 --> 01:11:12,800 where it is more or less likely to be, 1613 01:11:12,800 --> 01:11:14,830 but it doesn't tell me where it will be. 1614 01:11:14,830 --> 01:11:17,040 It can't tell me that. 1615 01:11:17,040 --> 01:11:19,170 Psi squared only tells me a probability. 1616 01:11:19,170 --> 01:11:21,000 It only tells me-- 1617 01:11:21,000 --> 01:11:22,620 it can tell me where it can never be. 1618 01:11:25,413 --> 01:11:26,330 That's what these are. 1619 01:11:26,330 --> 01:11:27,620 Those are those zeros. 1620 01:11:27,620 --> 01:11:31,790 When psi squared is zero, that electron can never be there. 1621 01:11:31,790 --> 01:11:35,390 But it also can tell me with more likelihood or less 1622 01:11:35,390 --> 01:11:36,990 where I might find it. 1623 01:11:36,990 --> 01:11:39,390 So if I measure it 10 times, well, most of the time, 1624 01:11:39,390 --> 01:11:40,265 I'll find it in here. 1625 01:11:40,265 --> 01:11:43,960 Maybe once I find it kind of out here. 1626 01:11:43,960 --> 01:11:45,850 That's the nature of quantum mechanics. 1627 01:11:45,850 --> 01:11:48,400 That's the relationship between the psi that we're going 1628 01:11:48,400 --> 01:11:54,860 to solve for and the real deal. 1629 01:11:54,860 --> 01:11:58,490 Now, what you find, then, is see, the 1s is here, 1630 01:11:58,490 --> 01:11:59,820 and then the 2s is here. 1631 01:11:59,820 --> 01:12:05,080 So these are those allowable energy levels 1632 01:12:05,080 --> 01:12:07,780 for the atom, which we'll start with that next time. 1633 01:12:07,780 --> 01:12:11,350 But-- wait, don't go, we're not done yet. 1634 01:12:11,350 --> 01:12:16,500 So now, I've said that the system is quantized, 1635 01:12:16,500 --> 01:12:20,100 which means it can only have certain energies. 1636 01:12:20,100 --> 01:12:24,000 That's what the boundary conditions do. 1637 01:12:24,000 --> 01:12:27,090 How does that solve my classical atom problem? 1638 01:12:27,090 --> 01:12:30,662 The atom only living for 10 to the minus 12th seconds. 1639 01:12:30,662 --> 01:12:31,620 How does it solve that? 1640 01:12:43,800 --> 01:12:48,540 So basically-- yeah. 1641 01:12:48,540 --> 01:12:51,610 AUDIENCE: It can't radiate away just a little bit of energy. 1642 01:12:51,610 --> 01:12:55,222 It can't fall in just a little bit. 1643 01:12:55,222 --> 01:12:56,680 If it's going to radiate energy, it 1644 01:12:56,680 --> 01:12:58,270 has to fall down an entire level. 1645 01:12:58,270 --> 01:12:58,840 JEFFREY GROSSMAN: Exactly. 1646 01:12:58,840 --> 01:12:59,350 Yeah. 1647 01:12:59,350 --> 01:13:00,910 That's exactly right. 1648 01:13:00,910 --> 01:13:05,530 These electrons-- it solves the problem 1649 01:13:05,530 --> 01:13:08,140 of the electron collapsing into the core 1650 01:13:08,140 --> 01:13:10,540 because it says the electron no longer can collapse 1651 01:13:10,540 --> 01:13:13,090 into the core, basically. 1652 01:13:13,090 --> 01:13:15,340 We've quantized it, so it just can't do that. 1653 01:13:15,340 --> 01:13:18,400 Because you see, here's the 2s. 1654 01:13:18,400 --> 01:13:20,470 And then the 2p-- 1655 01:13:20,470 --> 01:13:22,270 you see, there's s, and there's 2s, 1656 01:13:22,270 --> 01:13:25,160 and then the 2p has some shape to it. 1657 01:13:25,160 --> 01:13:26,440 I'm just going to put wiggles. 1658 01:13:26,440 --> 01:13:28,040 It's not just a sphere anymore. 1659 01:13:28,040 --> 01:13:29,920 It's got shape. 1660 01:13:29,920 --> 01:13:32,020 When you go up higher in energy, that psi 1661 01:13:32,020 --> 01:13:34,940 squared has funny shapes. 1662 01:13:34,940 --> 01:13:38,560 But the point is that the probability distribution 1663 01:13:38,560 --> 01:13:43,570 is maybe around here, and it goes pretty much to zero. 1664 01:13:43,570 --> 01:13:46,365 It goes very close to zero in between, pretty much zero, 1665 01:13:46,365 --> 01:13:48,490 where the chance is like the age of the universe it 1666 01:13:48,490 --> 01:13:49,760 won't happen. 1667 01:13:49,760 --> 01:13:52,840 And so what that says is that that electron 1668 01:13:52,840 --> 01:13:55,840 is just not allowed to be here. 1669 01:13:55,840 --> 01:13:57,490 It cannot be there physically. 1670 01:13:57,490 --> 01:13:59,470 It cannot be in that part of space. 1671 01:13:59,470 --> 01:14:01,600 How cool is that? 1672 01:14:01,600 --> 01:14:03,910 I mean, how weird is that, right? 1673 01:14:03,910 --> 01:14:10,030 The electrons simply cannot exist in between the 2s 1674 01:14:10,030 --> 01:14:10,780 and the 1s. 1675 01:14:10,780 --> 01:14:13,930 They got to be at those energies. 1676 01:14:13,930 --> 01:14:15,970 You cannot give it an energy in between. 1677 01:14:15,970 --> 01:14:21,040 It won't take it, because the allowed levels are quantized. 1678 01:14:21,040 --> 01:14:23,080 There is no in-between. 1679 01:14:23,080 --> 01:14:25,620 [? Buber ?] was wrong. 1680 01:14:25,620 --> 01:14:26,750 How many of you know-- 1681 01:14:26,750 --> 01:14:27,770 never mind. 1682 01:14:27,770 --> 01:14:29,270 Nobody reads Buber. 1683 01:14:29,270 --> 01:14:30,605 Philosopher. 1684 01:14:30,605 --> 01:14:31,730 It's all in the in-between. 1685 01:14:31,730 --> 01:14:34,320 Never mind. 1686 01:14:34,320 --> 01:14:38,280 Point being that that's really mind-blowing, I think. 1687 01:14:38,280 --> 01:14:41,370 The electron cannot-- now here's the question. 1688 01:14:41,370 --> 01:14:45,220 Well, how does it get from 2s to 1s? 1689 01:14:45,220 --> 01:14:48,130 How does it get there if it's not allowed to go in between? 1690 01:14:53,300 --> 01:14:53,990 OK. 1691 01:14:53,990 --> 01:14:55,580 These are the interpretations-- we'll 1692 01:14:55,580 --> 01:14:57,270 pick up with that on Thursday. 1693 01:14:57,270 --> 01:14:58,520 These are the interpretations. 1694 01:14:58,520 --> 01:14:59,100 Look at that. 1695 01:14:59,100 --> 01:15:00,470 It's like a whole world. 1696 01:15:00,470 --> 01:15:02,450 It's incredible, all the discussion 1697 01:15:02,450 --> 01:15:05,480 on how to interpret psi and the different things. 1698 01:15:05,480 --> 01:15:06,740 And this is a great one. 1699 01:15:06,740 --> 01:15:09,050 They don't know they're doing quantum mechanics, 1700 01:15:09,050 --> 01:15:11,765 but that is a double slit kind of statement. 1701 01:15:14,270 --> 01:15:17,930 And finally, this is what we talked about, 1702 01:15:17,930 --> 01:15:21,210 and there's some great books. 1703 01:15:21,210 --> 01:15:23,390 There's also many, many places on the web 1704 01:15:23,390 --> 01:15:26,030 where you can read more about this. 1705 01:15:26,030 --> 01:15:28,520 And on Thursday, we're going to start 1706 01:15:28,520 --> 01:15:30,853 going more and more into how we can solve this 1707 01:15:30,853 --> 01:15:33,020 for real materials, which is where we're going to be 1708 01:15:33,020 --> 01:15:35,200 in this part of the class.