Pages
Some of the problems are adapted from or assigned from the required textbook:
Griffiths, David J. Introduction to Quantum Mechanics. Pearson Prentice Hall, 2004. ISBN: 9780131118928.
SES# | TOPICS | KEY DATES |
---|---|---|
Part 1: Time Independent Perturbation Theoryand WKB Approximation | ||
L1 | Time Independent Perturbation Theory | |
L2 | Time Independent Perturbation Theory (continued) | |
L3 | Degenerate Perturbation Theory |
Problem Set 1 due |
L4 | Hydrogen Atom Fine Structure | |
L5 | Hydrogen Atom Fine Structure (continued) |
Problem Set 2 due |
L6 | Zeeman Effect and Introduction to the Semiclassical Approximation | |
L7 | The Semiclassical WKB Approximation |
Problem Set 3 due |
L8 | WKB (continued). Airy Functions and Connection Formulae | |
L9 | Time Dependent Perturbation Theory |
Problem Set 4 due |
Part 2: Time Dependent Perturbation Theory and Adiabatic Approximation | ||
L10 | Fermi’s Golden Rule | |
L11 | Fermi’s Golden Rule for Harmonic Transitions |
Problem Set 5 due |
E1 | Mid-Term Exam | |
L12 | Hydrogen Ionization (completed). Light and Atoms | Final Paper Proposal due |
L13 | Light and Atoms (continued). Charged Particles in Electromagnetic Fields | |
L14 | Charged Particles in Electromagnetic Fields (continued) | |
L15 | Adiabatic Approximation |
Problem Set 6 due |
Peer Edit Session | ||
L16 | Adiabatic Approximation (continued) | Final Paper Draft due |
L17 | Adiabatic Approximation: Berry’s Phase | |
L18 | Adiabatic Approximation: Molecules | Problem Set 7 due |
Part 3: Scattering and Identical Particles | ||
L19 | Scattering | |
L20 | Scattering (continued 1) | |
L21 | Scattering (continued 2) | |
L22 | Scattering (continued 3). Identical Particles | Problem Set 8 due |
L23 | Identical Particles (continued 1) | |
L24 | Identical Particles (continued 2) | Final Papers returned |
Review for Final Exam | ||
E2 | Final Exam |
Chapter 1: Perturbation Theory (PDF)
Chapter 2: Hydrogen Fine Structure (PDF)
Chapter 3: Semiclassical Approximation (PDF)
Chapter 4: Time Dependent Perturbation Theory (PDF - 1.1MB)
Chapter 5: Particles in Electromagnetic Fields [not available]
Chapter 6: Adiabatic Approximation (PDF)
Chapter 7: Scattering (PDF)
Chapter 8: Identical Particles (PDF)
Required Text
[Griffiths] = Griffiths, David J. and Darrell F. Schroeter. Introduction to Quantum Mechanics. Cambridge, United Kingdom: Cambridge University Press, 2018. ISBN: 9781107189638.
References
[Cohen-Tannoudji] = Cohen-Tannoudji, Claude, et. al. Quantum Mechanics, Vol. 2. Wiley, 1991. ISBN: 9780471164357.
[Shankar] = Shankar, Ramamurti. Principles of Quantum Mechanics. Plenum Press, 2011. ISBN: 9780306447907.
[Sakurai] = Sakurai, J. J. Modern Quantum Mechanics. Cambridge University Press, 2017. ISBN: 9781108422413.
WEEK # | READING |
---|---|
1 |
[Griffiths] Chapter 6 [Cohen-Tannoudji] Chapter XI [Shankar] Chapter 17 [Sakurai] Sections 5.1-5.3 |
2 |
[Griffiths] Chapter 6 [Cohen-Tannoudji] Chapter XI and Chapter XII [Shankar] Chapter 17 |
3 |
[Griffiths] Sections 6.3, 6.4, and 6.5 [Cohen-Tannoudji] Chapter XII [Shankar] Chapter 17 |
4 |
[Griffiths] Chapter 8 on WKB approximation [Shankar] Section 16.2 |
5 |
[Griffiths] Chapter 9 [Cohen-Tannoudji] Chapter XIII and/or [Shankar] Chapter 18 |
6 | [No readings] |
7 | [No readings] |
8 | [Griffiths] Sections 9.2 and 9.3 for interactions of atoms with light. Chapter 10 for the adiabatic approximation. |
9 |
[Cohen-Tannoudji] Chapter VI Complement E, which has a nice treatment of Landau levels. [Sakurai] pp. 130-139 [Shankar]’s treatment of Landau levels begins from Page 587. |
10 | [No readings] |
11 |
[Griffiths] Chapter 11 [Cohen-Tannoudji] Chapter VIII and/or [Shankar] Chapter 19 |
12 | [No readings] |
13 |
[Griffiths] Chapter 5 Optional:
|
Course Meeting Times
Lectures: 2 sessions / week, 90 minutes / session
Recitations: 2 sessions / week, 1 hour / session
Prerequisites
Students must have completed 8.05 Quantum Physics II with a grade of C or higher.
Course Goal
By the end of this course, you will be able to interpret and analyze a wide range of quantum mechanical systems using both exact analytic techniques and various approximation methods. This course is a continuation of 8.05 Quantum Physics II, and will introduce some of the important model systems studied in contemporary physics, including two-dimensional electron systems, the fine structure of hydrogen, lasers, and particle scattering.
Required Text
Griffiths, David J. and Darrell F. Schroeter. Introduction to Quantum Mechanics. Cambridge, United Kingdom: Cambridge University Press, 2018. ISBN: 9781107189638.
References
Cohen-Tannoudji, Claude, et. al. Quantum Mechanics, Vol. 2. Wiley, 1991. ISBN: 9780471164357. (Highly recommended) Vol.1. is also good.
Merzbacher, Eugen. Quantum Mechanics. Wiley, 2005. ISBN: 9788126533176. (Highly recommended)
Shankar, Ramamurti. Principles of Quantum Mechanics. Plenum Press, 2011. ISBN: 9780306447907. (Recommended)
Sakurai, J. J. Modern Quantum Mechanics. Cambridge University Press, 2017. ISBN: 9781108422413.
Schumacher, Benjamin, and Michael D. Westmoreland. Quantum Processes, Systems, and Information. Cambridge University Press, 2010. ISBN: 9780521875349.
Feynman, Richard. P. Feynman Lectures On Physics. Vol. 3. Basic Books, 2011. ISBN: 9780201021158.
Ohanian, Hans. Principles of Quantum Mechanics. Prentice Hall, 1989. ISBN: 9780137127955.
Problem Sets
There will be nine graded problem sets, and one ungraded problem set for the last week of class. Problem sets will be posted on the course website at least one week before they are due. Solutions will be available on the course website the day after the problem set is due. Graded problem sets will be returned in recitation,
For practical, not punitive, reasons, late homework will not be graded under any circumstances. This is especially important if you think you might want to change from listener to credit status. For conflicts that are known in advance, such as religious holidays or travel, problem sets should be turned in before the deadline. If you are away from MIT, you may submit your problem set electronically, as long as you alert theTeaching Assistant ahead of time. To allow for unforeseen circumstances such as illness or emergencies, one problem set will be dropped from the homework average, either an omitted set or the one with the lowest score. We strongly recommend that you nevertheless turn in all of the psets, and that even if you are unable to turn one in, that you work through the problems on your own anyway.
Problem sets are a very important part of this class. We believe that sitting down yourself and trying to reason your way through a problem not only helps you learn the material deeply, but also develops analytical tools fundamental to a successful career in science. We recognize that students also learn a great deal from talking to and working with each other. We therefore encourage each student to make his/her own attempt on every problem and then, having done so, to discuss the problems with one another and collaborate on understanding them more fully. After you have understood the problem, it is essential for your understanding to write up the solution completely by yourself. It is a breach of academic integrity to copy any solution from another student or from previous years solutions. Your solutions should be logical, complete and legible. If you cannot present a solution clearly, it is likely that you do not understand it adequately. The graders are instructed not to give credit for unclear or illegible solutions.
Exams
There will be a 1.5-hour closed-book midterm exam and one three-hour final exam. [Note: Exams are not available to OCW users.]
Term Paper
A highlight of this course is the term paper, which offers an opportunity to study in depth a quantum mechanical system not covered in the regular coursework. Every student will be expected to research, write and “publish” a short paper on a topic related to the content of Quantum Physics II or III.
The paper can explain a physical effect or further explicate ideas or problems covered in the courses. It can be based on the student’s own calculations and/or library research. The paper should be written in the style and format of a brief journal article and should aim at an audience of Quantum Physics III students. Writing, editing, revising, and “publishing” skills are an integral part of the project, which is described in full in a separate handout.
Because this course is a CI-M (Communication Intensive in the Major) Subject, in order to pass, you must obtain a grade of C or better on your term paper. If you do not succeed in this, you will get a grade of Incomplete until you revise your term paper sufficiently to earn at least a C, and only at that time you will be assigned a final grade based on the breakdown given above.
Grading
activities | percentages |
---|---|
Problem Sets | 25% |
Midterm | 15% |
Term Paper | 25% |
Final Exam | 35% |
The faculty may alter grades to reflect class participation, improvement, effort, attendance, and other qualitative measures of performance.
Note that this course is not graded on any predetermined curve. If the class as a whole shows exceptional mastery of quantum mechanics, the grades will be exceptionally high. Since we use absolute rather than relative standards, it is impossible for a student to lower his or her grade by helping classmates understand the material. Indeed, the process of explaining difficult concepts to a colleague can significantly help clarify and solidify one’s own understanding. Typically, students perform best when they regularly attend lectures and recitations, consistently turn in quality problems sets, put in sustained effort for their term paper, and leave adequate time for exam preparation.
Project Summary
Everyone in this course will be expected to research, write and “publish” a short paper on a topic related to the content of 8.05 Quantum Physics II or 8.06 Quantum Physics III. The paper can explain a physical effect or further explicate ideas or problems covered in the courses. It can be based on the student’s own calculations and/or library research. The paper should be written in the style and format of a brief journal article and should aim at an audience of 8.06 students.
Writing, editing, revising and “publishing” skills are an integral part of the project. Each of you will ask another student to edit your draft and will then prepare a final draft on the basis of the suggestions of your “peer editor.” We will supply templates for the RevTeX version of LaTeX (used by the Journal Physical Review) so that you can prepare your paper in a finished, publishable, form. In there is sufficient demand, we can also arrange a LaTeX tutorial.
You will submit your first draft marked up with editorial comments by your peer editor. This first draft will then be critiqued by a “writing assistant” (see below) and returned to you. Two weeks after the first draft is due, you will submit your final draft. Your papers will be graded on the intellectual quality of your work, the effectiveness of your presentation and the success of your prose style. A part of your grade will also be determined by how carefully and constructively you edited the draft of the paper for which you were the peer editor. The grade you earn for your paper will count 25% towards your final grade.
Because 8.06 is a CI-M Subject (Communication Intensive in the Major), in order to pass you must obtain a grade of C or better on your term paper. If you do not succeed in this, you will get a grade of “Incomplete” until you revise your term paper sufficiently to earn at least a C, and only at that time you will be assigned a final grade, again with your term paper grade counting 25%.
A practicing physicist writing a research paper often asks a few colleagues to comment on a first draft. The final draft is then reviewed anonymously by one or several peers before it is accepted by a journal like the Physical Review. The goal of this informal and formal peer review process is to push authors to write papers which successfully communicate ideas among a community of peers. Your goal is to write a paper which presents a phenomenon or problem in quantum physics in a way which communicates your ideas clearly and effectively to your fellow 8.06 students, namely to your peers. If your peers cannot understand what you write, you have not succeeded. Note that writing for your peers is a much higher standard than writing for the faculty. Presenting a topic sufficiently clearly and logically that one of your peers new to this topic can learn about it requires clarity of thought and depth of understanding. These are the prerequisites for an effective written (or, for that matter, verbal) presentation.
We have “writing assistants” who can help you with writing, editing and preparing the paper. Each of you will be contacted by email by one of the writing assistants during the 8th week of the course. You should arrange to meet soon thereafter, and should seek their assistance from then on as you need it. They will critique the proposal and outline for your paper, and will also critique the first draft which you submit after it has been peer edited. In between, you may also ask them to help you with parts of your paper as you write them. Think of your writing assistant as a coach. They are there to help you, and are good at it.
By the time you turn in your final paper, it will have been edited by one of your peers and you will also have had time to implement the suggestions of one of the writing assistants. Past 8.06 students have found that their papers improve enormously through this process. Based on experience from previous years, by the time you turn in your finished paper, very many of you will have produced an account of a piece of physics written to a very high standard. It would be a shame if these papers were not “published.” We shall have as our goal the “publication” of a journal consisting of all your papers. Note that for publication it is important that you submit your paper electronically, using the LaTeX template provided. Subject to these caveats, we hope to produce a compilation of all of your papers. We will circulate this “journal” to all of you, so that you can, in the end, read the work of all your peers.
The videos in this course are broadly divided into three parts:
Part 1. Time Independent Perturbation Theory and WKB Approximation.
In this section, we discuss in detail non-degenerate and degenerate time-independent perturbation theory. As an application and illustration of the methods, we study the fine structure of the hydrogen atom as well as the Zeeman effect, both in its weak and strong forms. We develop the Wentzel-Kramers-Brillouin (WKB) approximation, useful for time-independent problems that involve potentials with slow-varying spatial dependence.
Part 2. Time Dependent Perturbation Theory and Adiabatic Approximation.
In this section, we begin by developing perturbation theory for time-dependent Hamiltonians. We then turn to Fermi’s Golden Rule, and then to the interaction of light with atoms, focusing on the processes of absorption, stimulated emission, and spontaneous emission. We discuss charged particles in electromagnetic fields and derive the Landau levels of a particle in a uniform magnetic field. We study in detail the Adiabatic approximation, discussing Landau-Zener transitions, Berry’s phase, and the Born-Oppenheimer approximation for molecules.
Part 3. Scattering and Identical Particles.
The final part of the course begins with a study of scattering. We discuss cross sections and develop the theory of partial waves and phase shifts. An integral reformulation of the scattering problem leads to the Born approximation. We then turn to the subject of identical particles. We explain the exchange degeneracy problem and develop the machinery of permutation operators, symmetrizers and anti-symmetrizers. We discuss the symmetrization postulate and discuss the construction and properties of multi particle bosonic and fermonic states.