PHYS 632
Quantum Mechanics

Winter Quarter 2009

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.

The course 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, Revised Edition, by J. J. Sakurai.

Reading:

• 5 to 9 January. Sakurai, sections 3.4 and 3.5. (Plus review sections 3.1, 3.2, 3.3.) See also the notes on the rotation group and quantum mechanics.
• 12 to 16 January. Sakurai, sections 3.4 and 3.5, continued. Note that we have not emphasized the Euler rotations; you should have a basic understanding of them, but do not need a detailed understanding.
• 19 to 23 January. Sakurai, section 3.6.
• 26 to 30 January. Sakurai, section 3.7 and 3.8.
• 2 to 6 February. Prepare for midterm exam on 6 February. Note additions to notes "The rotation group and quantum mechanics."
• 9 to 13 February. Sakurai, section 3.10. See also sections 13, 14, and 15 of the notes "The rotation group and quantum mechanics."
• 16 to 20 February. Sakurai, section 3.9 (Bell's inequality). Sections 16 and 17 of the notes "The rotation group and quantum mechanics," about Bell's inequality and about the hydrogen atom.
• 23 to 27 February. Sakurai, sections 4.1, 4.2, 4.3.
• 2 to 6 March. Sakurai, section 4.4.
• 9 to 13 March. We will study the density matrix in the case of a combined system made of separate parts. Then we will start with Sec. 5.1 of Sakurai and close with some review of the quarter.

Homework:

1. Monday 12 January. Exercises 3.1, 7.1, 7.2, 8.1 and 8.2 from the notes "The rotation group and quantum mechanics".
2. Wednesday 21 January. Problems 4, 10, and 11 from Chapter 3 of Sakurai.
3. Monday 26 January. 1) Derive Eqs. (3.6.9), (3.6.11), and (3.6.12) in Sakurai. 2) Starting from Eq. (3.6.36) in Sakurai, prove Eq. (3.6.37).
4. Monday 2 February. Consider the Clebsch-Gordon coefficients for combining spin j₁ = 5 and spin j₂ = 2 to make spin j = 4. Calculate the Clebsch-Gordon coefficient for m₁ = -2, m₂ = 1 and m = -1. I am looking for a numerical answer as a decimal number correct to four or five places. 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, but please write your own program. If you use Mathematica, you may want to consult the hints about some functions that you might use. You will also want to look at the Mathematica help files.
5. Monday 9 February. No assignment. Study for midterm exam on 6 February.
6. Wednesday 18 February. Problems 26, 27, and 28 from Chapter 3 of Sakurai.
7. Wednesday 25 February. Problems 16.1 and 16.2 from the notes "The rotation group and quantum mechanics".
8. Wednesday 4 March. Problems 1, 2, 3, and 6 from Chapter 4 of Sakurai.
9. Wednesday 11 March. Problems 9, 11, and 12 from Chapter 4 of Sakurai.

Available notes in .pdf and .nb format:

• Vectors for quantum mechanics (13 October 2008).
• Path integrals and the classical approximation (17 November 2008).
• The rotation group and quantum mechanics (18 February 2009).

Exams:

• Midterm Exam: Friday, 6 February, in class.
• Final Exam: 15:15 Monday 16 March.

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.