Physics 162b Quantum Mechanics

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Mildred Green
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1 Physics 162b Quantum Mechanics Contact details and office hours Syllabus for Winter/Spring 2019 Instructor: Albion Lawrence. Contact info. Office: Abelson 344. Phone: As a rule, I will not answer class-related in the evening, unless it involves a personal emergency or a serious mistake in a problem set; even then I am unlikely to see it until late. Class place and time: T-F 9:30-10:50, Abelson 229. I will likely miss two or three lectures over the course of the semester, for conferences or other professional travel. If so, makeup classes for those times and for any snow days will be negotiated as the come up. Office hours and review sessions: Will be negotiated the first day of class. I am also available by advanced appointment. Unfortunately, as department chair I am unable to accept walk-in visits unless it is a serious emergency that requires my immediate attention. Grader/TA: watch this space. Disabilities. If you are a student with a documented disability on record at Brandeis University and wish to have a reasonable accommodation made for you in this class, please see me immediately. Course description and learning goals. Physics 162b is a second-semester graduate course in advanced quantum mechanics. The focus is on applications of basic principles, and on various approximation schemes that capture different physical situations. Many of the approximation schemes we will study have applications outside of quantum mechanics, and we will discuss these as well. By the end of the course the students should understand and be able to use: perturbation theory to physical problems; variational methods for determining ground state properties of a system; approximations based on the existence of disparate time scales (the sudden, adiabatic, and Born-Oppenheimer approximation); symmetries in quantum mechanics as well as their role in organizing perturbation theory; and basic field quantization (for scalar and electromagnetic fields). If time permits they will understand and be able to use basic mean field-like techniques for studying many-body physics; and scattering theory. Success in this 4 credit hour course is based on the expectation that students will spend a minimum of 9 hours of study time per week in preparation for class (readings, papers, discussion sections, preparation for exams, etc.) Prerequisites. Physics 162a, or consent of the instructor. 1

2 Grading, exams, problem sets. Basis of grades: Problem sets, 40%; 1 in-class midterm, 10%; take-home final, 40%; additional spot quizzes, reading questions (questions based on reading/lectures and submitted to Latte), in-class presentations, etc. 10%;. Spot quizzes are there for me to make a point, or to test the students understanding of the material. They are usually unannounced and graded for effort. For problem sets, I will drop the problem set with the lowest percentage and base the grade on your total percentage of the remaining problem sets. Lectures: The core of this course is the in-class lectures, combined with in-class spot quizzes, short student presentations, and discussions. Although there is a required text, and you are expected to supplement the lectures with reading on your own, no book will be followed strictly, and the material will be presented from the point of view of a practicing physicist. (Though the subjects covered are standard). A certain amount of improvisation will occur depending on questions. It is important to come to class when you can. I m not taking attendance, but it is advisable to warn me in advance if you cannot attend, in case of a spot quiz or other activity based on student participation. I will only allow make-ups of in class work if the student has informed me in advance and I have given my assent; or if the student had a sudden illness or family emergency that they did not have time to inform me of. I will post (handwritten) lecture notes to Latte within a day or two after a given lecture. In the end the responsibility for learning the material is yours. In particular, please ask questions during class and office hours, especially if something I say is not clear (I m not always a good mind reader, so it is your job to tell me if you are lost). My personal experience as a student is that whenever I thought a question was too stupid, somebody else asked it and it was not stupid at all. Problem sets: Problem sets will be handed out for the most part weekly, due Friday by the beginning of class unless otherwise announced. Late problem sets will not be accepted unless there is an obvious emergency serious illness, family emergency, etc. or you will be out of town with a good reason (conference, wedding of yourself or immediate family member, visiting graduate schools) and you have discussed it with me and received my approval before the time the problem set is handed out. The problem sets will be challenging, as is typical for a graduate-level quantum mechanics course. Their intent is to help the students learn the subject; some things can only be learned by practice, and some points are best made by having the students work through a problem. I expect that you complete all of them. You are advised to start looking at the problem set and taking an initial crack at it early. First, you will know quickly what does and does not totally confuse you, and can either ask questions and do the needed background preparation (reading etc.) Secondly, if you spend some time attacking the problem early on, you may find that you keep working on them subconsciously. Finally, you will have enough time for the problems to be pedagogically effective. As a rule the problem sets will not be doable in 1 evening In particular, problem sets which you have more that 1 week to do will generally take more than 1 week to do. You are strongly encouraged to discuss the problem sets with your classmates. The work you hand in, however, must be your own. 2

3 Exams: Midterm date is TBA, close to the first week of March, and in-class. Take-home final TBA, likely during the final week of classes. Both exams will be open note and open book using only the assigned book. Additional books and internet resources of any kind are forbidden, as is discussion of the exams with other people before the exams are completed by everybody. In general the exams will be of a different character than the problem sets; they will test conceptual understanding. I will hand out sample problems in advance, to give some idea of my testing style. Additional evaluation criteria. I use a small set of tools to encourage active, real-time engagement with the material. Spot quizzes can either ask a question that prepares the students for a lecture; ask about material in a previous lecture, to test and consolidate the students understanding; or re-visit a problem set or exam question that a large number of students found confusion. These will be graded for serious effort. Reading questions are questions posted by the students to me, via Latte, based on specific readings or lectures. These are graded for serious effort. I will also call students (in random order) at various points to give a short presentation of a problem from the problem sets or exams, and to explain the answer to the spot quizzes. Again, these are graded for serious effort. Academic integrity. The work you turn in problem sets, exams, quizzes, and reading questions must be your own. Identical problem sets or exams will be considered as plagiarized and treated as such. Please consult Brandeis University Rights and Responsibilities for all policies and procedures related to academic integrity. Students may be required to submit work to TurnItIn.com software to verify originality. Allegations of alleged academic dishonesty will be forwarded to the Director of Academic Integrity. Sanctions for academic dishonesty can include failing grades and/or suspension from the university. 3

4 Course outline The schedule is a bit ambitious, and subject to change depending on how I feel the class is responding to the material. The material will be a synthesis of the assigned reading and the lectures. SP refers to Sakurai and Polito (the main text). I am not giving specific date projections for these subjects as I adjust the speed and level of detail to how well the class is responding. 1. Symmetries in quantum mechanics: (SP Ch. 4 + additional reading) (a) General theory: transformation groups, group representations, conservation laws, weakly broken symmetries, selection rules. (b) Angular momentum: spin and orbital momentum. Addition of angular momentum. (c) Isospin (d) Discrete symmetries: Parity, time reversal. 2. Time-independent perturbation theory and variational methods (SP ch additional reading) (a) Nondegenerate perturbation theory (b) Perturbation theory for simple classical problems (c) Degenerate and almost-degenerate perturbation theory (d) Variational methods 3. Time-dependent perturbation theory (SP additional reading): (a) The interaction picture. Dyson series. (b) First-order transitions and Fermi s Golden Rule. (c) Periodic perturbations. 4. Approximations based on separation of time scales. (SP additional reading). (a) Sudden approximation (b) The adiabatic approximation. (c) Berry s phase. (d) The Born-Oppenheimer approximation. 5. Interaction of matter and radiation (SP 5.8 plus additional reading): (a) Charged particles in a classical electromagnetic field: (b) Aharonov-Bohm effect. Quantum Hall effect. 6. Field quantization (Additional reading). 4

5 (a) Quantization of a scalar field. (b) Quantization of electromagnetic field (c) Interaction of charged matter and quantized electromagnetic field. 7. (if time). Approximations for many-electron atoms: Hartree, Hartree-Fock and Thomas- Fermi approximations. 8. (if time) Scattering theory (SP 6). Cross sections. Green functions The Born approximation. Bound states and resonances. 5

6 Reading. Required Book: Sakurai and Polito, Modern Quantum Mechanics. A standard textbook at this level, and the one used for 162a. I or others also recommend the following books, which will be placed on reserve along with a few others. Do let me know if there are others that you like. 1. Shankar, Principles of Quantum Mechanics. The required text for Physics 162a. It explains some subtle points very well, and is a good additional resource for seeing what is going on. 2. Baym s Lectures on Quantum Mechanics. While it has been around for a while, I really like this book, and often use it as the required text when I teach 162. It is very physical. Also the end-of-chapter problems are excellent. 3. Landau and Lifshitz, Quantum Mechanics (non-relativistic theory), 3rd edition. This is a beautiful book; it is old-fashioned but still quite useful. Its discussion of group theory in quantum mechanics, semiclassical/wkb methods, and scattering theory, are all superb. 4. P.A.M. Dirac, Principles of Quantum Mechanics. An important and beautifullywritten monograph laying out the basic concepts of quantum mechanics. Except for the final section on quantum field theory, it has never gone out of date. 5. E. Merzbacher, Quantum Mechanics. A classic. Solid, complete presentations. 6. A. Messiah, Quantum Mechanics. An older, fairly mathematical, and complete treatise. Recommended for scattering theory, and the adiabatic and Born-Oppenheimer approximations. 6

Physics 162b Quantum Mechanics

Physics 162b Quantum Mechanics Syllabus for Winter/Spring 2017 1 Course description Physics 162b is a second-semester graduate course in advanced quantum mechanics. We will open with some advanced topics