PHYS 632
Quantum Mechanics

Winter Quarter 2010

MWF at 13:00 at 318 Willamette.

This the second quarter of a one year graduate level course. The course page for the first quarter is available.

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, Revised Edition, by J. J. Sakurai.

Schedule:

• I will be out of town in Seattle Wednesday and Friday 13 and 15 January. We will reschedule those classes later in the quarter.
• There will be a makeup class at 4:00 pm on Friday 29 January in the ITS conference room.
• There will be a makeup class at 4:00 pm on Friday 19 February in the ITS conference room.

Reading:

• 4 - 8 January: Sakurai, sec. 3.5 plus notes The rotation group and quantum mechanics sections 9 and 10.
• 11 - 15 January: Notes The rotation group and quantum mechanics section 11, plus corresponding sections in Sakurai.
• 20 - 22 January: Notes The rotation group and quantum mechanics sections 12, 13, 14, 15, and 16, plus corresponding sections in Sakurai.
• 25 - 29 January: Notes The rotation group and quantum mechanics sections 17, 18, and 19, plus corresponding sections in Sakurai.
• 1-5 February: Notes The rotation group and quantum mechanics sections 20, 21, and 22, plus corresponding sections in Sakurai.
• 8-12 February: Sakurai section 3.4 on the density operator. (Plus midterm exam on Wednesday.)
• 15-19 February: Finish Sakurai chapter 3 and read Sakurai sections 4.1 and 4.2.
• 22-26 February: Continue with Sakurai section 4.2 and read Sakurai section 4.3.
• 1-5 March: Sakurai section 4.4.
• 8-12 March: Boost invariance from notes Galilean boost symmetry.

Homework:

1. Monday 11 January. Work out Exercises 11.1, 11.2, and 11.3 in the notes The rotation group and quantum mechanics. Note that there are some signs wrong in the previous version of these notes. If you see l(l+1) + m(m +/- 1), it should be l(l+1) - m(m +/- 1). Look for versions dated 9 January or later.
2. Wednesday 20 January. Work out Exercises 8.1, and 8.2 in the notes The rotation group and quantum mechanics.
3. Wednesday 27 January. Do Exercise 16.1 in the notes The rotation group and quantum mechanics. This exercise asks you to calculate some Clebsch-Gordon coefficients. I am looking for numerical answers to, say, four significant digits. You could do this by hand, but I don't recommend it. If you prefer to use some sort of computer program, please include the key parts of your program with a little explanation. I am pleased if you cooperate with each other on this, put please write your own program. If you use Mathematica, you may want to consults the hints about some functions that you might use. You will also want to consult the Mathematica help files.
4. Wednesday 3 February. Do Exercise 17.1 in the notes The rotation group and quantum mechanics. Again, this is a problem to do with your computer. Please include the key parts of your program with a little explanation. I am pleased if you cooperate with each other on this, put please write your own program.
5. Monday 8 February: Sakurai problems 27 and 28 in chapter 3.
6. Wednesday 17 February: Sakurai problems 3.10 and 3.11 plus problem 2 from the midterm exam from last year.
7. Wednesday 24 February: Sakurai problems 4.1, 4.2, and 4.3.
8. Wednesday 3 March: This problem.
9. Wednesday 10 March: Sakurai problems 4.9, 4.11, and 4.12. For 4.12, notice that how the state transforms under time reversal depends on the phase that you assign to it.

Available notes in .pdf and .nb format:

• Vectors for quantum mechanics (12 October 2009).
• Choice of units for quantum mechanics (16 October 2009).
• Position and momentum in quantum mechanics (23 October 2009).
• Path integrals and the classical approximation (18 November 2009).
• The rotation group and quantum mechanics (26 February 2010).
• Galilean boost symmetry (9 March 2010).

Exams:

• Midterm Exam: 13:00 Wednesday 10 February. You may want to look at the midterm exam from last year. Note that problem 2 was about the density operator, which we have not yet covered this year.
• Final Exam: 15:15 Thursday 18 March. You may want to look at the final exam from last year.

Grading:

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.