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 --> 00:00:16,575 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:16,575 --> 00:00:18,332 at ocw.mit.edu. 8 00:00:25,220 --> 00:00:28,550 JEFFREY GROSSMAN: So we're very excited about this class. 9 00:00:28,550 --> 00:00:31,430 And, excuse me, this is the only time 10 00:00:31,430 --> 00:00:33,050 I get you until after spring break. 11 00:00:33,050 --> 00:00:37,550 So I'm not going to-- well I'll see you, maybe, 12 00:00:37,550 --> 00:00:41,540 but in terms of this class, I come on after spring break 13 00:00:41,540 --> 00:00:43,565 and then I get you for the rest of the semester. 14 00:00:46,100 --> 00:00:48,440 And so what I want to do in the next 20 minutes 15 00:00:48,440 --> 00:00:52,320 is just give you a little preview of what's coming. 16 00:00:52,320 --> 00:00:54,350 Now, did you, Professor Wheeler, did you 17 00:00:54,350 --> 00:00:56,010 talk about laptops and stuff? 18 00:00:56,010 --> 00:00:58,460 So let me talk about that for a minute. 19 00:01:02,000 --> 00:01:06,880 Any of you who had me in 3012 know that, for me, what I 20 00:01:06,880 --> 00:01:09,380 would prefer is that when I'm lecturing, that you don't have 21 00:01:09,380 --> 00:01:11,720 your laptops open and you're not pulling 22 00:01:11,720 --> 00:01:14,000 your sort of under the table texting, unless-- 23 00:01:14,000 --> 00:01:15,200 now there is an exception. 24 00:01:15,200 --> 00:01:17,351 Who knows the exception? 25 00:01:17,351 --> 00:01:18,720 Can anybody remember? 26 00:01:18,720 --> 00:01:21,600 Nobody actually took me up on this last fall, 27 00:01:21,600 --> 00:01:25,140 but if you really feel so inspired by what 28 00:01:25,140 --> 00:01:27,300 I'm talking about or what we're talking about 29 00:01:27,300 --> 00:01:31,328 that you need to send a tweet and summarize it, 30 00:01:31,328 --> 00:01:33,870 or you need to broadcast this information that you're getting 31 00:01:33,870 --> 00:01:36,750 in the class out to more people to bring them in, 32 00:01:36,750 --> 00:01:39,720 then that's OK. 33 00:01:39,720 --> 00:01:42,060 Otherwise, I'd really prefer it because if you 34 00:01:42,060 --> 00:01:43,620 open your laptop, what you're doing 35 00:01:43,620 --> 00:01:45,037 is you're creating a field of view 36 00:01:45,037 --> 00:01:47,200 for all the people behind you to get distracted. 37 00:01:47,200 --> 00:01:49,298 Same with the phone under the table trick, right? 38 00:01:49,298 --> 00:01:50,340 A lot of people see that. 39 00:01:50,340 --> 00:01:52,080 It's a little distracting. 40 00:01:52,080 --> 00:01:55,830 The point of the class is discussion, right? 41 00:01:55,830 --> 00:01:58,380 So we're going to have slides, we're 42 00:01:58,380 --> 00:02:00,930 going to talk about slides, but if you don't ask questions, 43 00:02:00,930 --> 00:02:02,370 it's a lot less useful. 44 00:02:02,370 --> 00:02:03,690 You won't learn as much. 45 00:02:03,690 --> 00:02:07,620 So I really like getting interrupted. 46 00:02:07,620 --> 00:02:10,740 Just, like, yell out something. 47 00:02:10,740 --> 00:02:12,930 I don't know. 48 00:02:12,930 --> 00:02:15,030 In 3012, the key word was "entropy." 49 00:02:15,030 --> 00:02:18,150 You could yell out "entropy" any time, and I'd turn around 50 00:02:18,150 --> 00:02:19,770 and we'd talk. 51 00:02:19,770 --> 00:02:23,200 Here, it could be, like, "quantum" would be a good one, 52 00:02:23,200 --> 00:02:23,700 right? 53 00:02:23,700 --> 00:02:26,710 But I really want you to ask the question when you have it, 54 00:02:26,710 --> 00:02:28,800 because if we have a discussion on the spot 55 00:02:28,800 --> 00:02:31,110 about your question, that's a learning moment, right? 56 00:02:31,110 --> 00:02:33,190 That's a chance to learn more for everyone. 57 00:02:33,190 --> 00:02:34,700 So I mean, the studies are in. 58 00:02:34,700 --> 00:02:37,320 I'm not just being kind of touchy feely 59 00:02:37,320 --> 00:02:38,195 about learning here. 60 00:02:38,195 --> 00:02:39,570 There's a lot of rigorous studies 61 00:02:39,570 --> 00:02:41,100 about how people learn best. 62 00:02:41,100 --> 00:02:43,930 And it's in those discussions where you learn the most. 63 00:02:43,930 --> 00:02:46,140 So please, interact. 64 00:02:46,140 --> 00:02:48,240 Ask questions. 65 00:02:48,240 --> 00:02:50,940 Now I'm going to motivate quantum mechanics. 66 00:02:50,940 --> 00:02:56,220 And how many of you have seen quantum mechanics before? 67 00:02:56,220 --> 00:02:59,560 How many of you have never seen quantum mechanics? 68 00:02:59,560 --> 00:03:00,360 It's OK. 69 00:03:00,360 --> 00:03:02,490 See, the thing is, what's going to be really-- 70 00:03:02,490 --> 00:03:03,420 so here's the thing. 71 00:03:03,420 --> 00:03:05,550 You don't have to have seen quantum mechanics 72 00:03:05,550 --> 00:03:09,510 to feel your complete oneness and total enjoyment 73 00:03:09,510 --> 00:03:12,030 of the quantum mechanical simulations we're going to do. 74 00:03:12,030 --> 00:03:14,797 This is going to be really exciting whether you've 75 00:03:14,797 --> 00:03:17,130 seen quantum or not because we're going to kind of start 76 00:03:17,130 --> 00:03:19,440 slowly and then we're going to learn 77 00:03:19,440 --> 00:03:22,630 how to simulate the behavior of quantum mechanics. 78 00:03:22,630 --> 00:03:26,130 So what I want to do today is just tell you 79 00:03:26,130 --> 00:03:28,910 sort of why this is exciting and why this is important. 80 00:03:28,910 --> 00:03:31,166 OK? 81 00:03:31,166 --> 00:03:32,620 OK, so that's what-- 82 00:03:32,620 --> 00:03:34,540 and I'll give you a more detailed outline when 83 00:03:34,540 --> 00:03:36,907 I come on for my part after spring break, 84 00:03:36,907 --> 00:03:38,740 but those are sort of the highlights of what 85 00:03:38,740 --> 00:03:40,520 we're going to touch on. 86 00:03:40,520 --> 00:03:41,900 Now I thought that-- 87 00:03:41,900 --> 00:03:46,970 OK, so I think Professor Wheeler may have shown this, right? 88 00:03:46,970 --> 00:03:49,850 So did you show the computers? 89 00:03:49,850 --> 00:03:52,790 Does anybody know where the fastest computer on the planet 90 00:03:52,790 --> 00:03:53,880 is? 91 00:03:53,880 --> 00:03:55,400 We've gotten a lot faster, right? 92 00:03:55,400 --> 00:03:56,960 So some of these were actually here. 93 00:03:56,960 --> 00:03:58,130 The Whirlwind was here. 94 00:03:58,130 --> 00:04:00,213 So you can see the number of operations per second 95 00:04:00,213 --> 00:04:03,000 has increased dramatically, right? 96 00:04:03,000 --> 00:04:06,400 Where's the fastest computer in the world today? 97 00:04:06,400 --> 00:04:09,110 Good guess. 98 00:04:09,110 --> 00:04:09,860 Yeah. 99 00:04:09,860 --> 00:04:12,450 Anybody know who has it? 100 00:04:12,450 --> 00:04:13,830 It's Google, right? 101 00:04:13,830 --> 00:04:16,230 It's Google. 102 00:04:16,230 --> 00:04:18,149 And I keep emailing them, and they 103 00:04:18,149 --> 00:04:19,980 don't respond to my emails, because I 104 00:04:19,980 --> 00:04:21,750 want to get some cycles on that machine. 105 00:04:21,750 --> 00:04:23,610 But they actually need to build power plants 106 00:04:23,610 --> 00:04:25,500 for those computers. 107 00:04:25,500 --> 00:04:27,290 And Professor Wheeler showed that there's 108 00:04:27,290 --> 00:04:29,790 like one little rack where your simulations are going to go. 109 00:04:29,790 --> 00:04:32,730 Well Google has like thousands of those. 110 00:04:32,730 --> 00:04:37,440 Now I thought I'd share my own personal history here. 111 00:04:37,440 --> 00:04:39,315 Has anybody seen either of these in a museum? 112 00:04:42,660 --> 00:04:44,320 This is the good old days. 113 00:04:44,320 --> 00:04:46,710 We used to call it the Trash-80. 114 00:04:46,710 --> 00:04:48,098 It was a couple of years ago. 115 00:04:48,098 --> 00:04:50,640 But that's how I grew up, just working on machines like this. 116 00:04:50,640 --> 00:04:52,290 And then there was this one which had 117 00:04:52,290 --> 00:04:53,910 a cartridge you could put in. 118 00:04:53,910 --> 00:04:55,890 You could save your data to a tape. 119 00:04:55,890 --> 00:04:56,695 OK? 120 00:04:56,695 --> 00:04:57,570 Do you remember that? 121 00:04:57,570 --> 00:04:58,780 No, you're too young. 122 00:04:58,780 --> 00:04:59,610 Yeah. 123 00:04:59,610 --> 00:05:04,740 So now, when you save data to a tape, you literally are-- like, 124 00:05:04,740 --> 00:05:06,660 you guys think about megabytes, gigabytes. 125 00:05:06,660 --> 00:05:09,240 You would save like a 10k file and it 126 00:05:09,240 --> 00:05:11,190 would take you 10 minutes, OK? 127 00:05:11,190 --> 00:05:12,570 And it would have these beeps. 128 00:05:12,570 --> 00:05:15,910 Anyway, someday you can check it out in the museum. 129 00:05:15,910 --> 00:05:20,400 But my favorite is the startup screen, right? 130 00:05:20,400 --> 00:05:22,950 So this one would just come on and it would say "ready." 131 00:05:22,950 --> 00:05:23,910 I like that. 132 00:05:23,910 --> 00:05:24,480 Right? 133 00:05:24,480 --> 00:05:25,590 So those are the old days. 134 00:05:29,950 --> 00:05:32,890 OK, so Professor Wheeler talked about this. 135 00:05:32,890 --> 00:05:35,280 He talked about how I'm not even on here. 136 00:05:35,280 --> 00:05:36,460 I'm all the way down here. 137 00:05:36,460 --> 00:05:37,030 Hey. 138 00:05:37,030 --> 00:05:37,530 You know? 139 00:05:37,530 --> 00:05:39,910 But last but not least, right? 140 00:05:39,910 --> 00:05:44,020 Bottom but really important, because we're 141 00:05:44,020 --> 00:05:46,210 talking about bottom-up materials understanding 142 00:05:46,210 --> 00:05:49,600 and design, and this level-- understanding and being 143 00:05:49,600 --> 00:05:51,340 able to compute this level is going 144 00:05:51,340 --> 00:05:53,590 to be important for all the rest of the levels, right? 145 00:05:53,590 --> 00:05:55,900 Now, what we're going to talk about when 146 00:05:55,900 --> 00:05:58,150 I come on in the second half is not just 147 00:05:58,150 --> 00:05:59,170 those potentials, right? 148 00:05:59,170 --> 00:06:04,190 So quantum mechanics gets you those potentials between atoms 149 00:06:04,190 --> 00:06:06,500 that you can then feed into there to there to there 150 00:06:06,500 --> 00:06:10,250 to there, but it also gets you real materials behaviors 151 00:06:10,250 --> 00:06:14,060 directly that you cannot get in any other way. 152 00:06:14,060 --> 00:06:18,940 Somebody tell me a quantum mechanical object that's 153 00:06:18,940 --> 00:06:22,310 just like really quantumy. 154 00:06:22,310 --> 00:06:25,250 What makes you think quantum? 155 00:06:25,250 --> 00:06:27,980 Electrons, yes. 156 00:06:27,980 --> 00:06:28,520 I love that. 157 00:06:28,520 --> 00:06:29,353 That's another word. 158 00:06:29,353 --> 00:06:31,280 If you want to say electrons any time, 159 00:06:31,280 --> 00:06:33,170 in the middle of a sentence, say electrons. 160 00:06:33,170 --> 00:06:34,100 Scream it out. 161 00:06:34,100 --> 00:06:35,570 That's it, right? 162 00:06:35,570 --> 00:06:39,020 Electrons are quantum mechanical objects, right? 163 00:06:39,020 --> 00:06:40,880 You really need quantum mechanics 164 00:06:40,880 --> 00:06:42,960 to know what an electron is doing. 165 00:06:42,960 --> 00:06:45,290 And it turns out that knowing what an electron is doing 166 00:06:45,290 --> 00:06:47,790 is really important for a lot of properties, OK? 167 00:06:47,790 --> 00:06:52,220 So I'm going to give you a sense of that in this little preview 168 00:06:52,220 --> 00:06:53,000 today. 169 00:06:53,000 --> 00:06:54,690 OK, so we're all the way down there. 170 00:06:54,690 --> 00:07:00,050 Now there are a lot of quantum mechanists and some of you 171 00:07:00,050 --> 00:07:02,010 may recognize some of these people. 172 00:07:02,010 --> 00:07:03,020 So these are the people. 173 00:07:03,020 --> 00:07:05,810 And you can tell, in contrast to thermodynamicists, 174 00:07:05,810 --> 00:07:10,290 they don't have mutton chops, right? 175 00:07:10,290 --> 00:07:12,680 And I don't know that we could say there's a trend here. 176 00:07:12,680 --> 00:07:14,000 I mean they look nice here. 177 00:07:14,000 --> 00:07:14,600 A little less. 178 00:07:14,600 --> 00:07:18,260 Well anyway, they look-- these were some really smart people. 179 00:07:18,260 --> 00:07:21,320 These are revolutionizing sort of the way we 180 00:07:21,320 --> 00:07:23,250 understand and view the world. 181 00:07:23,250 --> 00:07:26,330 And we'll talk about what their contributions were as we 182 00:07:26,330 --> 00:07:27,930 sort of start the quantum part. 183 00:07:27,930 --> 00:07:28,430 OK? 184 00:07:31,790 --> 00:07:33,320 And we'll talk about the problems. 185 00:07:33,320 --> 00:07:36,750 You see, because they had this thing for a long time. 186 00:07:36,750 --> 00:07:37,250 Right? 187 00:07:37,250 --> 00:07:39,800 They had classical physics which described the world really 188 00:07:39,800 --> 00:07:41,360 well. 189 00:07:41,360 --> 00:07:45,120 Did we need quantum mechanics to send people to the moon? 190 00:07:45,120 --> 00:07:47,780 Turns out, no, right? 191 00:07:47,780 --> 00:07:49,850 So we can do a lot without quantum mechanics, 192 00:07:49,850 --> 00:07:51,980 but there started to become these problems 193 00:07:51,980 --> 00:07:54,620 that classical mechanics couldn't describe. 194 00:07:54,620 --> 00:07:56,498 OK, and so we'll talk about those as well. 195 00:07:56,498 --> 00:07:58,040 I'm not going to talk about them now. 196 00:07:58,040 --> 00:08:00,500 But those problems became so great, 197 00:08:00,500 --> 00:08:04,010 that it just sort pushed these great thinkers 198 00:08:04,010 --> 00:08:06,800 of the time, of 100 years ago into developing 199 00:08:06,800 --> 00:08:08,450 a completely new theory for the world, 200 00:08:08,450 --> 00:08:09,700 for the way we view the world. 201 00:08:12,230 --> 00:08:15,470 Here's one of the funny things about quantum mechanics. 202 00:08:15,470 --> 00:08:17,090 This is a quantum mechanical ball. 203 00:08:17,090 --> 00:08:19,310 And I just threw it into a wall. 204 00:08:19,310 --> 00:08:21,080 Right, and look at what happened. 205 00:08:21,080 --> 00:08:23,420 Now, we'll talk about this later. 206 00:08:23,420 --> 00:08:25,670 A quantum mechanical ball is not a ball. 207 00:08:25,670 --> 00:08:27,920 It's a spread out thing, right? 208 00:08:27,920 --> 00:08:31,460 It has a probability associated with it. 209 00:08:31,460 --> 00:08:33,260 But look at what happens there, right? 210 00:08:33,260 --> 00:08:34,963 Look at this. 211 00:08:34,963 --> 00:08:35,630 What's going on? 212 00:08:35,630 --> 00:08:37,690 Somebody tell me what's happening. 213 00:08:37,690 --> 00:08:38,659 What is it? 214 00:08:38,659 --> 00:08:39,644 Tunneling. 215 00:08:39,644 --> 00:08:44,660 Now, is tunneling something that happens in like real systems 216 00:08:44,660 --> 00:08:46,670 and materials? 217 00:08:46,670 --> 00:08:48,380 Yeah, you bet it does. 218 00:08:48,380 --> 00:08:50,010 Electrons do it all the time. 219 00:08:50,010 --> 00:08:53,240 And if you can't predict this kind of tunneling behavior 220 00:08:53,240 --> 00:08:57,362 correctly then you can't design optoelectronic materials, 221 00:08:57,362 --> 00:08:58,820 right, at least if you want to know 222 00:08:58,820 --> 00:09:02,300 what the electrons are going to do, which is pretty important. 223 00:09:02,300 --> 00:09:07,270 OK, now, it turns out that, OK, so that's 224 00:09:07,270 --> 00:09:09,730 a quantum mechanical ball thrown into a wall. 225 00:09:09,730 --> 00:09:11,110 Uh-oh, OK. 226 00:09:11,110 --> 00:09:13,632 And then there is this very simple reaction 227 00:09:13,632 --> 00:09:15,340 that shows the behavior of the electrons. 228 00:09:15,340 --> 00:09:17,530 We already saw that, so I'm going to skip that. 229 00:09:17,530 --> 00:09:20,110 But so this can be complex, right? 230 00:09:20,110 --> 00:09:22,240 Things are going like through walls. 231 00:09:22,240 --> 00:09:23,530 That's weird. 232 00:09:23,530 --> 00:09:25,590 Isn't that kind of weird? 233 00:09:25,590 --> 00:09:28,060 I mean, that's weird. 234 00:09:28,060 --> 00:09:29,530 If I throw a ball into a wall, you 235 00:09:29,530 --> 00:09:32,350 don't usually expect part of it to keep going, right? 236 00:09:32,350 --> 00:09:33,910 You expect it to bounce back. 237 00:09:33,910 --> 00:09:36,310 But if I throw an electron into that wall, some of it 238 00:09:36,310 --> 00:09:38,140 will keep going, right? 239 00:09:38,140 --> 00:09:39,820 And this is even weirder. 240 00:09:39,820 --> 00:09:42,820 If I start mixing materials together and reacting them, 241 00:09:42,820 --> 00:09:46,390 those electrons can behave really, really weirdly. 242 00:09:46,390 --> 00:09:47,470 That's quantum mechanics. 243 00:09:47,470 --> 00:09:53,740 And we'll come to feel our enjoyment and oneness 244 00:09:53,740 --> 00:09:54,880 with that weirdness. 245 00:09:54,880 --> 00:09:56,020 It's really fun actually. 246 00:09:56,020 --> 00:09:59,830 It's really fun to think about how weird it is. 247 00:09:59,830 --> 00:10:03,523 The nice sort of thing, and also the really hard thing 248 00:10:03,523 --> 00:10:05,440 about quantum mechanics is that there's really 249 00:10:05,440 --> 00:10:07,540 only one equation that we're going to care about. 250 00:10:07,540 --> 00:10:09,160 This is it. 251 00:10:09,160 --> 00:10:13,140 Right, that's the Schrodinger equation. 252 00:10:13,140 --> 00:10:16,365 And you can see that it's just a partial differential equation. 253 00:10:16,365 --> 00:10:19,440 It shouldn't be so bad, right? 254 00:10:19,440 --> 00:10:23,348 Well, so it turns out that this equation tells us everything 255 00:10:23,348 --> 00:10:25,140 that we need to know for quantum mechanics. 256 00:10:25,140 --> 00:10:26,790 It tells us about this thing. 257 00:10:26,790 --> 00:10:28,265 That's the wave function. 258 00:10:28,265 --> 00:10:30,150 OK, and the wave function is the word 259 00:10:30,150 --> 00:10:33,400 we use to describe that ball, that quantum mechanical ball. 260 00:10:33,400 --> 00:10:35,873 OK, it's that weird shape, right? 261 00:10:35,873 --> 00:10:38,040 And it turns out that if we can solve that equation, 262 00:10:38,040 --> 00:10:39,450 then I can get the shape of PSI. 263 00:10:39,450 --> 00:10:41,730 And then I know a lot about the quantum mechanics 264 00:10:41,730 --> 00:10:43,440 of the system. 265 00:10:43,440 --> 00:10:50,250 Now, here's what happens when you try to solve that equation. 266 00:10:50,250 --> 00:10:52,570 Here's this equation written in very simple form, 267 00:10:52,570 --> 00:10:53,472 H PSI equals E PSI. 268 00:10:53,472 --> 00:10:54,430 Don't worry about that. 269 00:10:54,430 --> 00:10:57,840 We'll get to that when we talk about quantum mechanics 270 00:10:57,840 --> 00:11:00,670 in the second half of the class. 271 00:11:00,670 --> 00:11:05,640 Again, we're not going to do sort of like quantum 101. 272 00:11:05,640 --> 00:11:13,380 We're going to really talk about the key essence of quantum 273 00:11:13,380 --> 00:11:13,890 mechanics. 274 00:11:13,890 --> 00:11:14,390 OK? 275 00:11:14,390 --> 00:11:17,640 We're not going to go into great detail of mathematics of it. 276 00:11:17,640 --> 00:11:19,530 OK, but it's basically a simple equation 277 00:11:19,530 --> 00:11:20,650 that you need to solve. 278 00:11:20,650 --> 00:11:22,560 So here is that quantum mechanical ball. 279 00:11:22,560 --> 00:11:25,020 This is just representing that wave. 280 00:11:25,020 --> 00:11:25,520 Right? 281 00:11:25,520 --> 00:11:27,130 This is a plane wave. 282 00:11:27,130 --> 00:11:29,450 And I'm throwing it into a wall. 283 00:11:29,450 --> 00:11:31,640 And I just happen to put another wall behind it, 284 00:11:31,640 --> 00:11:33,770 spaced like that, right? 285 00:11:33,770 --> 00:11:35,480 Now, how would you solve that equation? 286 00:11:38,460 --> 00:11:40,050 What's the first thing you might try? 287 00:11:43,110 --> 00:11:44,260 Don't say ask Siri. 288 00:11:44,260 --> 00:11:47,250 Actually, you could ask Siri. 289 00:11:47,250 --> 00:11:51,030 Wolfram Alpha Pro is coming out. 290 00:11:51,030 --> 00:11:54,830 So could you put this in a Mathematica? 291 00:11:54,830 --> 00:11:55,330 Right? 292 00:11:55,330 --> 00:11:56,700 Yeah. 293 00:11:56,700 --> 00:11:57,480 You could, right? 294 00:11:57,480 --> 00:11:58,360 It's an equation. 295 00:11:58,360 --> 00:11:59,400 It's got boundaries. 296 00:11:59,400 --> 00:12:00,900 It's got initial conditions. 297 00:12:00,900 --> 00:12:02,820 And here's what you get, OK. 298 00:12:02,820 --> 00:12:04,320 So that's a quantum mechanical ball. 299 00:12:04,320 --> 00:12:05,970 It's the simplest one you could get. 300 00:12:05,970 --> 00:12:08,820 It's just a little shape that you throw into two walls. 301 00:12:08,820 --> 00:12:11,350 And these are the equations you have to solve. 302 00:12:11,350 --> 00:12:14,110 Now, the fun part about this, which the students in this 303 00:12:14,110 --> 00:12:17,110 class two years ago did not think was that fun when I gave 304 00:12:17,110 --> 00:12:22,430 this on a homework assignment was that Wolfram Alpha cannot 305 00:12:22,430 --> 00:12:22,930 handle it. 306 00:12:22,930 --> 00:12:26,650 Wolfram, Mathematica, Matlab, you name it, chokes, right? 307 00:12:26,650 --> 00:12:29,740 You cannot solve these eight equations and eight unknowns 308 00:12:29,740 --> 00:12:32,427 unless you do some tricks, and [INAUDIBLE] tricks first. 309 00:12:32,427 --> 00:12:34,510 I won't give another problem like this, I promise. 310 00:12:34,510 --> 00:12:37,450 But the point of this was not meant 311 00:12:37,450 --> 00:12:39,042 to drive the students crazy. 312 00:12:39,042 --> 00:12:40,250 That really wasn't the point. 313 00:12:40,250 --> 00:12:43,780 The point was just to illustrate how hard this equation actually 314 00:12:43,780 --> 00:12:46,970 turns out to be to solve, OK? 315 00:12:46,970 --> 00:12:47,750 It looks simple. 316 00:12:47,750 --> 00:12:50,450 It's deceivingly simple. 317 00:12:50,450 --> 00:12:53,840 We can't solve it even today without making approximations. 318 00:12:53,840 --> 00:12:57,170 And the only reason we can solve it today for real materials 319 00:12:57,170 --> 00:13:00,920 is because we've figured out how to make really important 320 00:13:00,920 --> 00:13:06,740 algorithmic approximations, OK? 321 00:13:06,740 --> 00:13:11,015 The only Nobel Prize given in computation was given for that. 322 00:13:11,015 --> 00:13:13,640 I think that might be on my next slide. 323 00:13:13,640 --> 00:13:16,180 And computers have gotten really fast. 324 00:13:16,180 --> 00:13:17,680 OK, so I'm skipping ahead of myself. 325 00:13:21,100 --> 00:13:22,080 This is a quote. 326 00:13:22,080 --> 00:13:23,820 So before that, before we figured out 327 00:13:23,820 --> 00:13:26,340 how to solve that equation for real materials, 328 00:13:26,340 --> 00:13:30,190 people like Dirac, really smart people 329 00:13:30,190 --> 00:13:32,600 were feeling a little bit hopeless. 330 00:13:32,600 --> 00:13:35,830 Right, 1929, "The underlying physical laws 331 00:13:35,830 --> 00:13:37,630 necessary for the mathematical theory 332 00:13:37,630 --> 00:13:40,030 of a large part of physics and the whole of chemistry 333 00:13:40,030 --> 00:13:42,310 are thus completely known." 334 00:13:42,310 --> 00:13:43,310 What's he talking about? 335 00:13:43,310 --> 00:13:46,170 What's completely known? 336 00:13:46,170 --> 00:13:46,920 Yeah, how? 337 00:13:46,920 --> 00:13:49,550 How come? 338 00:13:49,550 --> 00:13:50,450 Right? 339 00:13:50,450 --> 00:13:51,800 They had kind of nailed it. 340 00:13:51,800 --> 00:13:56,030 Right, like in the late 1800s, they 341 00:13:56,030 --> 00:13:58,220 were like looking at the world and saying, why? 342 00:13:58,220 --> 00:13:59,880 This doesn't compute. 343 00:13:59,880 --> 00:14:02,810 And then they sort of spent 30 years developing the theory 344 00:14:02,810 --> 00:14:03,975 of quantum mechanics. 345 00:14:03,975 --> 00:14:06,350 And that's why he's saying it's kind of completely known. 346 00:14:06,350 --> 00:14:08,690 And the difficulty is only that the exact application 347 00:14:08,690 --> 00:14:10,910 of these laws leads to equations, much too 348 00:14:10,910 --> 00:14:12,900 complicated to be soluble. 349 00:14:12,900 --> 00:14:13,400 Right? 350 00:14:13,400 --> 00:14:16,070 That was 1929. 351 00:14:16,070 --> 00:14:19,472 He did say later if there's no complete agreement 352 00:14:19,472 --> 00:14:21,680 between the results of one's work and the experiment, 353 00:14:21,680 --> 00:14:24,320 one should not allow oneself to be too discouraged. 354 00:14:24,320 --> 00:14:26,630 I like that quote. 355 00:14:26,630 --> 00:14:29,600 It turns out that happens in simulation quite a bit, right? 356 00:14:29,600 --> 00:14:32,240 And that has to do with the fact that you can't 357 00:14:32,240 --> 00:14:33,800 solve the equations exactly. 358 00:14:33,800 --> 00:14:35,730 You have to make approximations. 359 00:14:35,730 --> 00:14:39,650 And knowing where you are in accuracy phase space 360 00:14:39,650 --> 00:14:42,180 is something that's very important in this class. 361 00:14:42,180 --> 00:14:44,080 And we'll be talking about that a lot. 362 00:14:44,080 --> 00:14:44,580 OK? 363 00:14:44,580 --> 00:14:46,550 But don't be discouraged. 364 00:14:46,550 --> 00:14:49,070 Nice words of encouragement from Dirac. 365 00:14:49,070 --> 00:14:52,558 OK, so that Nobel Prize I was talking about, 366 00:14:52,558 --> 00:14:53,600 that was actually shared. 367 00:14:53,600 --> 00:14:57,500 But one of the people who won it was Walter Cohn. 368 00:14:57,500 --> 00:15:01,400 And he won it because of an approximation, 369 00:15:01,400 --> 00:15:03,820 which I'll talk about a little bit 370 00:15:03,820 --> 00:15:06,120 when we go into quantum mechanics. 371 00:15:06,120 --> 00:15:08,103 And it turns out that you still can't 372 00:15:08,103 --> 00:15:09,770 solve the equations of quantum mechanics 373 00:15:09,770 --> 00:15:12,590 without making approximations. 374 00:15:12,590 --> 00:15:14,720 Even with the fastest comp-- 375 00:15:14,720 --> 00:15:17,810 how many transistors are on the fastest-- 376 00:15:17,810 --> 00:15:21,280 how many transistors can we put on a chip today? 377 00:15:21,280 --> 00:15:22,151 Does anybody know? 378 00:15:25,378 --> 00:15:26,170 10 billion? 379 00:15:26,170 --> 00:15:27,670 That's a good guess. 380 00:15:27,670 --> 00:15:30,110 I think 3 is where we're at. 381 00:15:30,110 --> 00:15:32,990 And how many neurons in your brain? 382 00:15:32,990 --> 00:15:35,180 100 billion, right? 383 00:15:35,180 --> 00:15:36,800 So we're getting close. 384 00:15:36,800 --> 00:15:38,960 We're getting real close. 385 00:15:38,960 --> 00:15:41,000 They're catching up, man. 386 00:15:41,000 --> 00:15:46,520 It costs as much money to make a transistor 387 00:15:46,520 --> 00:15:49,130 on a chip with 3 billion transistors on it 388 00:15:49,130 --> 00:15:52,280 as it does to print a single letter in a newspaper. 389 00:15:52,280 --> 00:15:55,910 OK, so we are very good at printing lots of transistors. 390 00:15:58,520 --> 00:16:01,970 That has dramatically accelerated how much CPU power 391 00:16:01,970 --> 00:16:02,600 we have. 392 00:16:02,600 --> 00:16:06,590 And it's still worthless, worthless for the equations 393 00:16:06,590 --> 00:16:09,982 of quantum mechanics, unless you make simplifications. 394 00:16:09,982 --> 00:16:12,440 So we're going to have to talk about those simplifications. 395 00:16:12,440 --> 00:16:14,673 Because they're still not solvable unless you make 396 00:16:14,673 --> 00:16:15,590 these simplifications. 397 00:16:15,590 --> 00:16:17,720 And that's why the Nobel Prize was given for it. 398 00:16:17,720 --> 00:16:20,024 That's how important it is. 399 00:16:20,024 --> 00:16:20,840 OK? 400 00:16:20,840 --> 00:16:25,070 Once you do that, once you know the model, 401 00:16:25,070 --> 00:16:27,530 once you develop that model that Professor Wheeler talked 402 00:16:27,530 --> 00:16:29,390 about for quantum mechanics, then 403 00:16:29,390 --> 00:16:31,610 you can go ahead and do simulations. 404 00:16:31,610 --> 00:16:34,650 And you can get some really interesting properties out. 405 00:16:34,650 --> 00:16:37,910 Like in this case, this is lead titanate. 406 00:16:37,910 --> 00:16:40,430 And there's some really interesting magnetic properties 407 00:16:40,430 --> 00:16:42,413 that have to do with where those electrons are. 408 00:16:42,413 --> 00:16:44,330 So I'm going to just give you a couple of sort 409 00:16:44,330 --> 00:16:51,050 of motivational slides for why understanding these electrons 410 00:16:51,050 --> 00:16:52,280 is so important. 411 00:16:52,280 --> 00:16:55,380 OK, and then I'll stop. 412 00:16:55,380 --> 00:16:58,780 How many know what this is? 413 00:16:58,780 --> 00:17:00,930 Yeah. 414 00:17:00,930 --> 00:17:02,200 Quantum dots? 415 00:17:02,200 --> 00:17:02,700 Yeah. 416 00:17:02,700 --> 00:17:03,670 What's happening here? 417 00:17:03,670 --> 00:17:06,334 Why are they different colors? 418 00:17:06,334 --> 00:17:07,709 AUDIENCE: Different energy bands. 419 00:17:10,083 --> 00:17:11,750 JEFFREY GROSSMAN: OK, and somebody said, 420 00:17:11,750 --> 00:17:13,720 what's the reason for that? 421 00:17:13,720 --> 00:17:15,900 Different sizes. 422 00:17:15,900 --> 00:17:17,089 Different sizes. 423 00:17:17,089 --> 00:17:18,780 Isn't that weird? 424 00:17:18,780 --> 00:17:21,905 Why is that? 425 00:17:21,905 --> 00:17:25,230 AUDIENCE: [INAUDIBLE] 426 00:17:25,230 --> 00:17:28,950 JEFFREY GROSSMAN: That's a good try. 427 00:17:28,950 --> 00:17:30,480 Not quite right. 428 00:17:30,480 --> 00:17:31,690 Good guess. 429 00:17:31,690 --> 00:17:34,020 Any other ideas? 430 00:17:34,020 --> 00:17:38,060 Well, there's always the go to answer, quantum. 431 00:17:38,060 --> 00:17:39,800 It's quantum mechanics. 432 00:17:39,800 --> 00:17:40,580 Right? 433 00:17:40,580 --> 00:17:42,180 It's quantum mechanics. 434 00:17:42,180 --> 00:17:44,660 This is red and that's blue. 435 00:17:44,660 --> 00:17:45,620 Aqua? 436 00:17:45,620 --> 00:17:46,250 Purple? 437 00:17:46,250 --> 00:17:47,240 I don't know. 438 00:17:47,240 --> 00:17:50,780 Because of quantum mechanics, right? 439 00:17:50,780 --> 00:17:52,930 Let's break that down. 440 00:17:52,930 --> 00:17:54,700 It has to do with-- 441 00:17:54,700 --> 00:17:56,620 this isn't really breaking that down, 442 00:17:56,620 --> 00:17:59,840 but it's related because it's nanotechnology. 443 00:17:59,840 --> 00:18:00,340 OK? 444 00:18:00,340 --> 00:18:03,130 So I'm going to explain that in just a minute. 445 00:18:03,130 --> 00:18:05,200 Nanotechnology. 446 00:18:05,200 --> 00:18:07,000 Well, you all know about nanotechnology. 447 00:18:07,000 --> 00:18:10,240 The scientist in Spider-Man was a nanotechnologist. 448 00:18:10,240 --> 00:18:11,410 Did you know that? 449 00:18:11,410 --> 00:18:16,600 And The Incredible Hulk, because of nanotechnology, right? 450 00:18:16,600 --> 00:18:27,940 So that's how Hollywood views nanotechnology. 451 00:18:27,940 --> 00:18:29,492 But why am I telling you about nano? 452 00:18:29,492 --> 00:18:31,450 Well, because the effects I'm about to describe 453 00:18:31,450 --> 00:18:32,480 is because of nanotechnology. 454 00:18:32,480 --> 00:18:33,980 You hear a lot about nanotechnology, 455 00:18:33,980 --> 00:18:35,720 and there's a lot of hype around it. 456 00:18:35,720 --> 00:18:38,093 There's also a lot of there there, OK? 457 00:18:38,093 --> 00:18:40,510 And I love this, in case you haven't seen the size scales. 458 00:18:40,510 --> 00:18:42,580 I know you've probably all seen too much nano. 459 00:18:42,580 --> 00:18:44,350 But I love this one where you're sitting 460 00:18:44,350 --> 00:18:47,610 on top of some random dude, and then you go out. 461 00:18:47,610 --> 00:18:48,610 Have you guys seen this? 462 00:18:48,610 --> 00:18:51,070 10 times, 100 times, 1,000, right? 463 00:18:51,070 --> 00:18:54,280 And you keep going out, OK, and that's 464 00:18:54,280 --> 00:18:57,280 how far you are when you go out by 10 to the 9th. 465 00:18:57,280 --> 00:19:01,020 And then you start again and you go in by the same amount, 466 00:19:01,020 --> 00:19:01,520 right? 467 00:19:01,520 --> 00:19:03,395 And so that's sort of just trying to give you 468 00:19:03,395 --> 00:19:04,840 a sense of the scales, right? 469 00:19:04,840 --> 00:19:09,890 So that's nano is going in by the same amount you'd be going 470 00:19:09,890 --> 00:19:11,240 out to get to here, right? 471 00:19:11,240 --> 00:19:12,020 It's kind of cool. 472 00:19:12,020 --> 00:19:14,030 It's small stuff. 473 00:19:14,030 --> 00:19:15,780 Why is that interesting? 474 00:19:15,780 --> 00:19:17,810 Oh, the press seems to know. 475 00:19:17,810 --> 00:19:19,880 It's because super cows and nanotechnology 476 00:19:19,880 --> 00:19:21,502 will make ice cream healthy. 477 00:19:21,502 --> 00:19:23,210 That's actually still my favorite article 478 00:19:23,210 --> 00:19:25,400 about nanotechnology. 479 00:19:25,400 --> 00:19:29,060 It's about healthy ice cream. 480 00:19:29,060 --> 00:19:31,370 Actually, my favorite part of this is the definition. 481 00:19:31,370 --> 00:19:32,900 I love this definition. 482 00:19:32,900 --> 00:19:36,080 It is also experimenting with nanotechnology or the science 483 00:19:36,080 --> 00:19:39,200 of invisibly tiny things. 484 00:19:39,200 --> 00:19:40,340 Right? 485 00:19:40,340 --> 00:19:41,150 We just saw them. 486 00:19:41,150 --> 00:19:42,080 They're red and blue. 487 00:19:42,080 --> 00:19:44,080 They're not invisible. 488 00:19:44,080 --> 00:19:49,300 OK, right, I highlighted it. 489 00:19:49,300 --> 00:19:51,080 OK, back to that example, right? 490 00:19:51,080 --> 00:19:52,960 So why am I connecting nano here? 491 00:19:52,960 --> 00:19:58,180 Well, because quantum feels nano a lot. 492 00:19:58,180 --> 00:20:01,400 Quantum and nano very often go hand in hand. 493 00:20:01,400 --> 00:20:03,233 Now, it depends how nano you mean. 494 00:20:03,233 --> 00:20:04,900 Some people say they're working on nano, 495 00:20:04,900 --> 00:20:06,525 and they're really at like 0.8 microns. 496 00:20:06,525 --> 00:20:08,650 That's sort of cheating, right? 497 00:20:08,650 --> 00:20:10,270 But not really. 498 00:20:10,270 --> 00:20:13,300 Hey, this is like some millions of nanometers. 499 00:20:13,300 --> 00:20:14,710 I guess that's working on nano. 500 00:20:14,710 --> 00:20:20,181 If I take a bulk semiconductor, what's a semiconductor? 501 00:20:23,620 --> 00:20:25,990 It's this picture. 502 00:20:25,990 --> 00:20:28,360 Somebody give me an example of a semiconductor material. 503 00:20:28,360 --> 00:20:29,110 AUDIENCE: Silicon? 504 00:20:29,110 --> 00:20:30,340 JEFFREY GROSSMAN: Silicon. 505 00:20:30,340 --> 00:20:31,120 Right? 506 00:20:31,120 --> 00:20:32,912 What are the properties of a semiconductor. 507 00:20:32,912 --> 00:20:35,200 Somebody tell me one property of a semiconductor. 508 00:20:35,200 --> 00:20:35,800 Yeah. 509 00:20:35,800 --> 00:20:36,860 AUDIENCE: [INAUDIBLE]. 510 00:20:38,960 --> 00:20:40,760 JEFFREY GROSSMAN: Yeah, yeah. 511 00:20:40,760 --> 00:20:42,140 It's got a gap. 512 00:20:42,140 --> 00:20:46,330 Not too big, not too small, just right. 513 00:20:46,330 --> 00:20:46,830 OK? 514 00:20:46,830 --> 00:20:48,420 We'll be coming back to that a lot, 515 00:20:48,420 --> 00:20:50,360 because that gap is something you can predict 516 00:20:50,360 --> 00:20:51,360 using quantum mechanics. 517 00:20:51,360 --> 00:20:54,760 You have to have quantum mechanics to predict it. 518 00:20:54,760 --> 00:20:58,980 Now, it turns out that if I look at this piece of silicon, 519 00:20:58,980 --> 00:21:02,330 it's optically not that exciting, right? 520 00:21:02,330 --> 00:21:05,390 That will go along with those different colors. 521 00:21:05,390 --> 00:21:07,140 Right, it just sort of looks like charcoal 522 00:21:07,140 --> 00:21:08,850 actually, unless you process it. 523 00:21:08,850 --> 00:21:11,900 Might be a little shiny, but it's kind of boring. 524 00:21:11,900 --> 00:21:15,540 If I take out my little nano ice cream scooper-- 525 00:21:15,540 --> 00:21:16,890 I'm a theorist, right? 526 00:21:16,890 --> 00:21:19,020 So this is how I view experiments. 527 00:21:19,020 --> 00:21:21,480 And you now scoop out a little piece of it. 528 00:21:21,480 --> 00:21:22,500 We have a name for that. 529 00:21:22,500 --> 00:21:24,985 That's called the quantum dot, right? 530 00:21:24,985 --> 00:21:25,860 That's a quantum dot. 531 00:21:25,860 --> 00:21:27,900 But it's nothing more than a little tiny piece. 532 00:21:27,900 --> 00:21:30,150 It's a nano piece, right? 533 00:21:30,150 --> 00:21:30,810 What happens? 534 00:21:30,810 --> 00:21:34,690 What happens is if you do that, that's when you get this. 535 00:21:34,690 --> 00:21:35,260 Right? 536 00:21:35,260 --> 00:21:35,760 Why? 537 00:21:38,300 --> 00:21:42,370 Back to our-- you know what the answer is. 538 00:21:42,370 --> 00:21:44,290 Quantum mechanics, OK? 539 00:21:44,290 --> 00:21:45,160 Here's the reason. 540 00:21:45,160 --> 00:21:49,120 Something called quantum confinement, OK? 541 00:21:49,120 --> 00:21:53,230 It turns out that if I create an optical excitation 542 00:21:53,230 --> 00:21:54,730 in this bulk semiconductor-- let's 543 00:21:54,730 --> 00:21:56,150 say I shine a laser on it. 544 00:21:56,150 --> 00:21:58,450 That's about the worst PowerPoint graphic 545 00:21:58,450 --> 00:21:59,080 I've ever seen. 546 00:22:01,990 --> 00:22:04,930 Anyway, but it's a laser. 547 00:22:04,930 --> 00:22:06,230 And you shine a light on it. 548 00:22:06,230 --> 00:22:09,940 Well, happens is, you see these little objects 549 00:22:09,940 --> 00:22:12,910 that I said were very quantum mechanical, the electron. 550 00:22:12,910 --> 00:22:13,600 Right? 551 00:22:13,600 --> 00:22:15,850 What happens is the energy from the light 552 00:22:15,850 --> 00:22:19,808 kicks an electron out of what's called its ground state. 553 00:22:19,808 --> 00:22:21,350 Well, we're going to talk about that. 554 00:22:21,350 --> 00:22:23,402 I'm getting really excited myself. 555 00:22:23,402 --> 00:22:25,360 And when it gets kicked out of its ground state 556 00:22:25,360 --> 00:22:29,080 it leaves behind a hole, or a positive charge, OK? 557 00:22:29,080 --> 00:22:30,550 So now you've got a negative charge 558 00:22:30,550 --> 00:22:34,060 and a positive charge that have been made in this material. 559 00:22:34,060 --> 00:22:36,070 They've been made by light. 560 00:22:36,070 --> 00:22:38,740 Why might I be excited about that? 561 00:22:38,740 --> 00:22:40,130 No pun intended [INAUDIBLE]. 562 00:22:40,130 --> 00:22:41,320 [LAUGHTER] 563 00:22:41,320 --> 00:22:42,730 Thank you, one person. 564 00:22:46,420 --> 00:22:49,750 If you've suffered through me last fall then, you know it. 565 00:22:49,750 --> 00:22:51,947 So why might I be excited about that? 566 00:22:51,947 --> 00:22:53,140 AUDIENCE: Solar power? 567 00:22:53,140 --> 00:22:54,307 JEFFREY GROSSMAN: Thank you. 568 00:22:54,307 --> 00:22:55,210 Solar power! 569 00:22:55,210 --> 00:22:57,550 We just made electricity from sunlight. 570 00:22:57,550 --> 00:23:02,170 Now, it turns out that electron, that positive and negative 571 00:23:02,170 --> 00:23:04,970 charge like to be a certain distance apart. 572 00:23:04,970 --> 00:23:08,620 Right, and bulk silicon, 5 nanometers. 573 00:23:08,620 --> 00:23:10,590 Right, it's called the exciton radius. 574 00:23:10,590 --> 00:23:12,550 When you create an electron hole pair, 575 00:23:12,550 --> 00:23:14,618 they kind of like each other. 576 00:23:14,618 --> 00:23:16,410 Well, they're very weakly bound in silicon. 577 00:23:16,410 --> 00:23:19,490 But they have a distance that they like to hang out, 578 00:23:19,490 --> 00:23:20,750 in this case 5 nanometers. 579 00:23:20,750 --> 00:23:22,880 And what that means is that when I run out 580 00:23:22,880 --> 00:23:27,750 of real estate in the material, and I do the same thing, 581 00:23:27,750 --> 00:23:29,630 well, they don't have anywhere to be. 582 00:23:29,630 --> 00:23:31,760 They want to be out here, but they 583 00:23:31,760 --> 00:23:34,070 can't be, because there's no material out there. 584 00:23:34,070 --> 00:23:36,980 Right, so if I'm less than that exciton radius, 585 00:23:36,980 --> 00:23:41,100 then my excitation is squeezed. 586 00:23:41,100 --> 00:23:42,100 We have a name for that. 587 00:23:42,100 --> 00:23:44,030 It's actually called quantum confinement. 588 00:23:44,030 --> 00:23:44,530 Why? 589 00:23:44,530 --> 00:23:47,050 Because these are very quantum mechanical objects. 590 00:23:47,050 --> 00:23:50,005 You need quantum mechanics to describe them. 591 00:23:50,005 --> 00:23:51,880 And what you've done is you've squeezed them. 592 00:23:51,880 --> 00:23:54,140 You've increased their kinetic energy. 593 00:23:54,140 --> 00:23:58,030 And that is the reason the color changes. 594 00:23:58,030 --> 00:24:01,120 That's the reason the band gap changes. 595 00:24:01,120 --> 00:24:03,790 And so you can see that the physical confinement 596 00:24:03,790 --> 00:24:07,750 of this excited state leads to this very unique quantum 597 00:24:07,750 --> 00:24:15,050 effect, which is that the light emitted depends on size, right? 598 00:24:15,050 --> 00:24:18,290 One example of many, of sort of the beauty that 599 00:24:18,290 --> 00:24:19,790 comes from understanding the quantum 600 00:24:19,790 --> 00:24:21,832 mechanics, and we're going to be able to simulate 601 00:24:21,832 --> 00:24:23,700 this in the second part of this class. 602 00:24:23,700 --> 00:24:24,380 OK? 603 00:24:24,380 --> 00:24:29,030 Now, that is a really useful piece of technology. 604 00:24:29,030 --> 00:24:30,408 Quantum dots are being used-- 605 00:24:30,408 --> 00:24:32,450 does anybody know about the uses of quantum dots? 606 00:24:32,450 --> 00:24:34,350 I mean, they're already in companies, right? 607 00:24:34,350 --> 00:24:34,850 Yeah. 608 00:24:34,850 --> 00:24:35,840 AUDIENCE: Solar cells. 609 00:24:35,840 --> 00:24:39,630 JEFFREY GROSSMAN: Solar cells, right? 610 00:24:39,630 --> 00:24:43,830 LED TVs, biomarkers. 611 00:24:43,830 --> 00:24:45,060 It's big in the biotech. 612 00:24:45,060 --> 00:24:46,050 Oh, sorry. 613 00:24:46,050 --> 00:24:47,552 I just stole your answer. 614 00:24:47,552 --> 00:24:48,760 And I didn't want to do that. 615 00:24:48,760 --> 00:24:50,450 Any other ideas? 616 00:24:50,450 --> 00:24:51,992 They're really useful, right? 617 00:24:51,992 --> 00:24:53,700 And they're getting more and more useful. 618 00:24:53,700 --> 00:24:57,840 Very interesting, all quantum mechanics. 619 00:24:57,840 --> 00:25:00,090 That gets me really excited, because I work on energy. 620 00:25:00,090 --> 00:25:03,840 And I'm not going to do an energy talk, don't worry. 621 00:25:03,840 --> 00:25:07,050 But I work a lot on energy. 622 00:25:07,050 --> 00:25:11,940 And the fact of the matter is that this is a map of the US. 623 00:25:11,940 --> 00:25:14,490 And it shows where there's good to excellent resources 624 00:25:14,490 --> 00:25:19,830 in some renewable technologies, like PV, red and orange. 625 00:25:19,830 --> 00:25:22,260 Biomass, green and light green. 626 00:25:22,260 --> 00:25:23,280 Wind. 627 00:25:23,280 --> 00:25:25,020 Number one most utilized renewable 628 00:25:25,020 --> 00:25:27,630 resource in the world today is wind, right? 629 00:25:27,630 --> 00:25:30,150 So if you look at this, there's only a few pockets 630 00:25:30,150 --> 00:25:31,920 where you're sort of-- 631 00:25:31,920 --> 00:25:35,760 sorry, man, it's gas or oil. 632 00:25:35,760 --> 00:25:38,700 Now, but we don't use hardly any of these resources, right? 633 00:25:38,700 --> 00:25:42,270 And the reason, as we all know, is cost and efficiency. 634 00:25:42,270 --> 00:25:46,140 But in so many of these technologies, not wind, 635 00:25:46,140 --> 00:25:49,500 in this case, but PV, biomass, and in a number 636 00:25:49,500 --> 00:25:51,960 of other technologies, solar fuels, 637 00:25:51,960 --> 00:25:55,750 the key is pushing electrons around. 638 00:25:55,750 --> 00:25:56,890 That's the key. 639 00:25:56,890 --> 00:25:59,740 It's pushing electrons up a hill, and letting the electrons 640 00:25:59,740 --> 00:26:02,450 fall down a hill, right? 641 00:26:02,450 --> 00:26:07,442 I mean, one of the oldest ways to store energy is what? 642 00:26:07,442 --> 00:26:08,910 Who knows? 643 00:26:08,910 --> 00:26:11,550 It goes way back. 644 00:26:11,550 --> 00:26:14,050 Still really used around the world, including the US. 645 00:26:14,050 --> 00:26:14,550 Yeah. 646 00:26:14,550 --> 00:26:15,605 AUDIENCE: Steam. 647 00:26:15,605 --> 00:26:16,980 JEFFREY GROSSMAN: Steam is a way. 648 00:26:16,980 --> 00:26:18,100 That's true. 649 00:26:18,100 --> 00:26:18,870 Think older. 650 00:26:21,380 --> 00:26:22,430 Pumping water. 651 00:26:22,430 --> 00:26:23,370 Who said that? 652 00:26:23,370 --> 00:26:23,870 In the back. 653 00:26:23,870 --> 00:26:25,010 Pumping water. 654 00:26:25,010 --> 00:26:26,930 You pump water up a hill. 655 00:26:26,930 --> 00:26:28,910 You hold it in a big lake. 656 00:26:28,910 --> 00:26:31,893 And you let it come down when you need energy, right? 657 00:26:31,893 --> 00:26:33,560 You pump it up when you have the energy, 658 00:26:33,560 --> 00:26:34,977 and let it come down when you need 659 00:26:34,977 --> 00:26:39,230 it is a terribly inefficient way to store energy, but it works. 660 00:26:39,230 --> 00:26:42,470 And basically, what we need to do for so many of these energy 661 00:26:42,470 --> 00:26:45,320 technologies is figure out how to more efficiently pump 662 00:26:45,320 --> 00:26:47,750 electrons up a hill. 663 00:26:47,750 --> 00:26:50,720 That's basically what we're doing, right? 664 00:26:50,720 --> 00:26:51,980 And that's quantum mechanics. 665 00:26:51,980 --> 00:26:55,040 Because by definition, electrons need quantum mechanics 666 00:26:55,040 --> 00:26:56,360 to describe. 667 00:26:56,360 --> 00:26:56,870 Right? 668 00:26:56,870 --> 00:27:00,230 So we're going to pump electrons up hills and around 669 00:27:00,230 --> 00:27:01,622 in the second part of this class. 670 00:27:01,622 --> 00:27:03,080 And you can tell your friends that. 671 00:27:03,080 --> 00:27:06,020 And it will impress them, I promise you. 672 00:27:06,020 --> 00:27:08,600 I always like to help you make conversation 673 00:27:08,600 --> 00:27:11,420 when you're at the bar. 674 00:27:11,420 --> 00:27:13,700 Because here's a solar cell. 675 00:27:13,700 --> 00:27:16,550 Do I have any time left? 676 00:27:16,550 --> 00:27:17,810 Yeah, I got a couple minutes. 677 00:27:17,810 --> 00:27:19,012 I'm almost done. 678 00:27:19,012 --> 00:27:19,970 I'm really almost done. 679 00:27:19,970 --> 00:27:21,200 Cause we're going to work on solar cells. 680 00:27:21,200 --> 00:27:23,283 First, we're going to spend sort of the first half 681 00:27:23,283 --> 00:27:26,510 of the quantum part learning about quantum, 682 00:27:26,510 --> 00:27:29,580 and how to simulate that equation, right? 683 00:27:29,580 --> 00:27:30,830 We're going to do simulations. 684 00:27:30,830 --> 00:27:34,340 And then we're going to apply those simulation 685 00:27:34,340 --> 00:27:35,780 tools to real problems. 686 00:27:35,780 --> 00:27:38,960 So we're going to study solar cells, for one. 687 00:27:38,960 --> 00:27:39,757 And look at this. 688 00:27:39,757 --> 00:27:41,090 Here is how a solar cells works. 689 00:27:41,090 --> 00:27:43,880 Well, that's what you see if you take like a core six class, 690 00:27:43,880 --> 00:27:45,880 and if you think about it from the device scale. 691 00:27:45,880 --> 00:27:48,080 But here's what's happening inside that solar cell. 692 00:27:48,080 --> 00:27:49,220 Sunlight comes in. 693 00:27:49,220 --> 00:27:51,740 Squiggly lines are always sunlight, right? 694 00:27:51,740 --> 00:27:52,970 Squiggly line comes in. 695 00:27:52,970 --> 00:27:55,350 And there is that electron. 696 00:27:55,350 --> 00:27:56,077 You can tell. 697 00:27:56,077 --> 00:27:56,910 Actually, you can't. 698 00:27:56,910 --> 00:27:57,930 But there it is. 699 00:27:57,930 --> 00:28:00,450 And it gets promoted up, cause that light 700 00:28:00,450 --> 00:28:03,930 has energy with it that knocks this electron up an energy. 701 00:28:03,930 --> 00:28:05,850 And look at what it left behind. 702 00:28:05,850 --> 00:28:09,180 A hole, just like I showed you in silicon, right? 703 00:28:09,180 --> 00:28:11,310 In those quantum dots. 704 00:28:11,310 --> 00:28:14,570 But in a solar cell, you don't want them to recombine and emit 705 00:28:14,570 --> 00:28:15,470 light. 706 00:28:15,470 --> 00:28:17,750 You don't want them to shine different colors. 707 00:28:17,750 --> 00:28:20,850 In a solar cell, you want to get those charges out. 708 00:28:20,850 --> 00:28:22,970 You want to get that electron out of one side, 709 00:28:22,970 --> 00:28:25,940 and get that hole out of the other side, right? 710 00:28:25,940 --> 00:28:28,550 Every single step here, converting the photon 711 00:28:28,550 --> 00:28:31,770 into an electron, electron and hole thermalize. 712 00:28:31,770 --> 00:28:33,690 They couple to the solar cell, and they 713 00:28:33,690 --> 00:28:36,637 waste all that energy coming back up to the valence 714 00:28:36,637 --> 00:28:37,470 and conduction band. 715 00:28:37,470 --> 00:28:40,260 They wasted all this heat, right? 716 00:28:40,260 --> 00:28:43,710 The electron hole pair diffuses. 717 00:28:43,710 --> 00:28:44,280 Hello there. 718 00:28:47,100 --> 00:28:49,670 Welcome to 302-1. 719 00:28:49,670 --> 00:28:51,620 This thing can move around. 720 00:28:51,620 --> 00:28:53,010 This pair can move around. 721 00:28:53,010 --> 00:28:53,510 And 722 00:28:53,510 --> 00:28:55,940 Then you've got to get them apart, right? 723 00:28:55,940 --> 00:28:58,280 And you got to get them out, right? 724 00:28:58,280 --> 00:29:00,620 Every single step that's critical 725 00:29:00,620 --> 00:29:02,420 is a quantum mechanical step. 726 00:29:02,420 --> 00:29:06,020 Right, you cannot describe these processes unless you can solve 727 00:29:06,020 --> 00:29:08,660 Schrodinger's equation, OK? 728 00:29:08,660 --> 00:29:10,325 So we'll be talking about that and how 729 00:29:10,325 --> 00:29:11,450 to make solar cells better. 730 00:29:11,450 --> 00:29:15,770 For example, in silicon, people put charts like this up. 731 00:29:15,770 --> 00:29:18,770 More than 80% of the solar cells you buy today are this. 732 00:29:18,770 --> 00:29:22,770 They're multi crystalline silicon, right? 733 00:29:22,770 --> 00:29:26,550 Now, the solar cells in your calculators 734 00:29:26,550 --> 00:29:28,440 are amorphous silicon. 735 00:29:28,440 --> 00:29:29,940 And the reason is, they're cheap. 736 00:29:32,638 --> 00:29:33,430 They're very cheap. 737 00:29:33,430 --> 00:29:35,170 But they're very inefficient. 738 00:29:35,170 --> 00:29:37,687 And so you see things-- but they could be thin and flexible. 739 00:29:37,687 --> 00:29:38,520 That's kind of nice. 740 00:29:38,520 --> 00:29:41,350 But they're just not that efficient. 741 00:29:41,350 --> 00:29:42,850 And so you start seeing things like, 742 00:29:42,850 --> 00:29:44,760 well, here, let's compare these two crystals. 743 00:29:44,760 --> 00:29:45,635 Here's a crystalline. 744 00:29:45,635 --> 00:29:46,350 Here's amorphous. 745 00:29:46,350 --> 00:29:47,733 There's a gap. 746 00:29:47,733 --> 00:29:49,150 Difference in energy between those 747 00:29:49,150 --> 00:29:52,940 states that the electron gets excited to, very different. 748 00:29:52,940 --> 00:29:54,370 There's absorption coefficients. 749 00:29:54,370 --> 00:29:55,130 Very different. 750 00:29:55,130 --> 00:29:55,970 There's mobilities. 751 00:29:55,970 --> 00:29:57,520 And this is actually what kills it. 752 00:29:57,520 --> 00:30:00,230 Those holes are so slow. 753 00:30:00,230 --> 00:30:00,740 Right? 754 00:30:00,740 --> 00:30:04,530 Well, how can you compute those things? 755 00:30:04,530 --> 00:30:05,690 Let me hear it. 756 00:30:05,690 --> 00:30:06,440 AUDIENCE: Quantum. 757 00:30:06,440 --> 00:30:09,200 JEFFREY GROSSMAN: Thank you, quantum mechanics. 758 00:30:09,200 --> 00:30:13,220 We can calculate, and we will calculate these things 759 00:30:13,220 --> 00:30:15,850 for these kinds of materials. 760 00:30:15,850 --> 00:30:19,030 And maybe you'll find a way to make amorphous silicon have 761 00:30:19,030 --> 00:30:21,210 faster holes. 762 00:30:21,210 --> 00:30:23,010 And if you do that, please come talk to me. 763 00:30:23,010 --> 00:30:23,610 [LAUGHTER] 764 00:30:23,610 --> 00:30:26,100 I'd be really interested, because I've been working 765 00:30:26,100 --> 00:30:28,585 on that problem for many years. 766 00:30:28,585 --> 00:30:30,210 But these are the kinds of things we're 767 00:30:30,210 --> 00:30:33,990 going to do, OK, in this class. 768 00:30:33,990 --> 00:30:35,410 And I'll tell you one quick story. 769 00:30:35,410 --> 00:30:37,230 I was at a conference on solar energy. 770 00:30:37,230 --> 00:30:39,990 And they gave out calculators as kind 771 00:30:39,990 --> 00:30:42,690 of solar powered calculators, solar energy calculators. 772 00:30:42,690 --> 00:30:44,850 Solar energy conference, solar powered calculators. 773 00:30:44,850 --> 00:30:47,400 And we opened one up. 774 00:30:47,400 --> 00:30:49,320 And it turned out it was battery powered. 775 00:30:49,320 --> 00:30:50,400 [LAUGHTER] 776 00:30:50,400 --> 00:30:53,820 And there was a little piece of amorphous silicon solar cell 777 00:30:53,820 --> 00:30:57,570 in there, but it wasn't wired up. 778 00:30:57,570 --> 00:31:01,310 And the reason is, these are so poor in their efficiencies, 779 00:31:01,310 --> 00:31:01,810 right? 780 00:31:01,810 --> 00:31:02,520 We've all seen it. 781 00:31:02,520 --> 00:31:03,750 You need to be in direct sun. 782 00:31:03,750 --> 00:31:05,260 And you can't see it anymore. 783 00:31:05,260 --> 00:31:05,760 Right? 784 00:31:05,760 --> 00:31:06,870 Why? 785 00:31:06,870 --> 00:31:09,762 If we could figure out how to boost that whole mobility, 786 00:31:09,762 --> 00:31:11,220 we could get their efficiencies up. 787 00:31:11,220 --> 00:31:12,178 They'd cost a lot less. 788 00:31:12,178 --> 00:31:13,823 We'd make a game changing difference. 789 00:31:13,823 --> 00:31:15,240 So these are the kinds of problems 790 00:31:15,240 --> 00:31:18,050 that we're going to work on in the second half.