PHYS 633
Quantum Mechanics

Spring Quarter 2012

MWF at 13:00 at 318 Willamette.

This the third quarter of a one year graduate level course. It is for students who have had an introductory course in quantum mechanics before. Students should also have a good background in mathematics, including linear algebra and complex analysis. I will start from the beginning and develop the major ideas of quantum mechanics. Thus a student who has not seen some particular idea or method will be able to learn it in this course. However, the pace will be too fast for a student who has not seen any of the ideas and methods.

Instructor:

Davison Soper
email: soper@uoregon.edu
phone: 6-5162
office: 479 Willamette.
office hours: Tuesdays and Thursdays 11:00-12:00.

Text:

Modern Quantum Mechanics, Second Edition, by J. J. Sakurai and Jim J. Napolitano.

Schedule:

There will be no class on Monday 2 April because some of our students will be taking the Ph.D. qualifying exam.
I need to be away on 28 May, 30 May, and 1 June. I will be at a workshop at DESY laboratory in Hamburg.
We will have makeup classes at 17:00 on Fridays: 20 April, 27 April, and 4 May.

Reading:

2 - 6 April. Sakurai, Chapter 7, sections 7.1 - 7.3. This is about the treatment of identical particles in quantum mechanics. We will return to other sections of chapter 7 later in the quarter.
9 - 13 April. Sakurai, Chapter 5, sections 5.1 - 5.2. Notes Perturbation theory for energy levels sections 1 and 2.
16 - 20 April. Sakurai, Chapter 5, sections 5.3 - 5.4. Notes The van der Waals interaction.
23 - 27 April. Sakurai, Chapter 5, section 5.5, the fist three subsections of section 5.6, and the first three subsections of 5.7. Notes Perturbation theory for energy levels sections 3 - 5. Notes The adiabatic approximation and Berry's phase.
30 April - 4 May. Sakurai, Chapter 5, section 5.7. Notes Time dependent perturbation theory sections 1 - 6.
7 - 11 May. Sakurai, Chapter 5, sections 5.8 - 5.9. Notes Time dependent perturbation theory sections 7 - 13.
14 - 18 May. Sakurai, Chapter 6, sections 6.1 - 6.3. Notes Scattering theory sections 1 - 9.
21 - 25 May. Sakurai, Chapter 6, sections 6.4 and 6.6. Notes Scattering theory sections 10 - 13 and 15.
28 May - 1 June. I will be at DESY laboraaory in Hamburg. No class.
4 - 8 June. Sakurai, Chapter 6, section 6.7. Notes Scattering theory sections 16 - 18. You may want to look at the exam from last year.

Homework:

There will be problems assigned each week in class, due on Wednesdays. Occasionally a problem will involve computer work. I recommend Mathematica, which is available at UO computer labs. If you already know some other computer language like C++, Fortran, Matlab, or Maple, you can use what you know.

Wednesday 11 April: Sakurai, problems 7.2, 7.3, 7.5, 7.6. For problem 7.3, we suppose that the spatial wave functions are the same for both of the particles. For problem 7.6, you can ignore the question "What is the total spin in each case."
Wednesday 18 April: Sakurai, problems 5.1, 5.2, 5.3, 5.4. (See solutions for problems 5.2, 5.3 and 5.4.)
Wednesday 25 April: Sakurai, problems 5.12, 5.20, 5.21. (See solution for problem 5.12.)
Wednesday 2 May: Sakurai, problems 5.22, 5.26, 5.30(a). Our midterm exam is also on 2 May. You may want to look at the midterm exam from last year. (See solution for problem 5.22.)
Wednesday 9 May: Sakurai, problems 5.35 and 5.38. (See solution for problem 5.38.)
Wednesday 16 May: Notes, Time dependent perturbation theory, exercise 12.1. (See solution.)
Wednesday 23 May: Notes, Scattering theory, exercise 6.1.
Wednesday 30 May: Notes, Sakurai problems 6.1 and 6.2. (Submit to Chris Newby.)
Wednesday 6 June: Notes, Scattering theory, exercises 15.1 and 15.2.

Available notes in .pdf format:

Vectors for quantum mechanics (5 October 2011).
Choice of units for quantum mechanics (10 October 2011).
Position and momentum in quantum mechanics (10 October 2011).
Path integrals and the classical approximation (14 November 2011).
The rotation group and quantum mechanics (30 January 2012).
The density operator in quantum mechanics (20 April 2012).
Perturbation theory for energy levels (5 April 2012).
The van der Waals interaction (20 April 2012).
Time dependent perturbation theory (11 May 2012).
The adiabatic approximation and Berry's phase (27 April 2012).
Scattering theory (6 June 2012).

Exams:

Midterm Exam: Wednesday 2 May, in class.
Final Exam: 15:15 Monday 11 June.

Grading:

The homework assignments will count for 25% of the course grade. There will be one midterm exam, which counts for 25% of the course grade. The final exam will count for 50% of the course grade.

Exams are to be taken without notes or books. That is because I want to encourage you to remember the most important formulas for quantum mechanics. If you will need an obscure complicated formula for an exam question, I will give it on the exam.

Note: I encourage students to work together on the homework. I don't want you to just copy from someone else's work because you won't learn anything that way, but if you work out the solution jointly with someone else or with a group, that's fine. Real science usually involves teamwork, so it's a good idea for you to learn how to work on science with others. This policy is an exception to the normal university rule about doing your own work. Of course, on exams, your paper has to be entirely your own work.

Davison E. Soper, Institute of Theoretical Science, University of Oregon, Eugene OR 97403 USA soper@uoregon.edu

PHYS 633 Quantum Mechanics