PHYS 631
Quantum Mechanics

Fall Quarter 2009

MWF at 13:00 at 318 Willamette.

This the first 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, Revised Edition, by J. J. Sakurai.

Schedule:

• I will be out of town on Monday 26 October to present a seminar for undergraduates at Humboldt State University in California. We will reschedule that class to Friday 30 October at 16:00 at the Institute of Theoretical Science conference room.
• I will be out of town on Friday 20 November for a meeting at Northwestern University of CTEQ, a research group that I belong to. We will reschedule that class to Friday 6 November at 16:00 at the Institute of Theoretical Science conference room.

Reading:

• 30 Sep - 2 Oct: Sakurai, Secs. 1.1 through 1.4. Notes, Vectors for quantum mechanics, Secs. 1 - 4.
• 5 - 9 Oct: Sakurai, Secs. 1.5. Notes, Vectors for quantum mechanics, Secs. 5 - 10.
• 12 - 16 Oct: Sakurai, Secs. 1.6 and 1.7. See also the notes on Choice of units for quantum mechanics and on Position and momentum in quantum mechanics.
• 19 - 23 Oct: Review all of chapter 1 of Sakurai and also the class notes as they exist on 23 October.
• 26 - 30 Oct: Sakurai, Secs. 2.1 and 2.2.
• 2 - 6 Nov: Sakurai, Secs. 2.3 and 2.4.
• 9 - 13 Nov: Sakurai, Sec. 2.5 plus notes on Path integrals and the classical approximation.
• 16 - 19 Nov: Sakurai, Sec. 2.6 plus notes on Path integrals and the classical approximation.
• 23 - 25 Nov: Sakurai, Complete Sakurai Sec. 2.6.
• 30 Nov - 4 Dec: Sakurai, Sakurai Sec. 3.1 and 3.2 plus notes on The rotation group and quantum mechanics sections 1 through 7.

Homework:

1. Wednesday 7 October. Exercises 1.1, 1.2, and 1.3 in the notes Vectors for quantum mechanics.
2. Wednesday 14 October. Exercise 1.4 and 1.5 in the notes Vectors for quantum mechanics. Sakurai, problems 1.1 and 1.13.
3. Wednesday 21 October. Sakurai, problems 1.19, 1.23, 1.29.
4. Wednesday 28 October. Midterm exam. In preparation, please try Sakurai problems 1.2 and 1.33 and problems 1 through 4 on the midterm exam from last year. However, do not turn your solutions in.
5. Wednesday 4 November. Sakurai, problems 2.1, 2.7, and 2.8.
6. Wednesday 11 November. Suppose that a particle is described at time zero by the gaussian wave function in position space in Eq. (75) of the notes "Position and momentum in quantum mechanics." For simplicity, take x₀ = 0. The particle evolves according to the free hamiltonian p²/(2m). Find a formula for the wave function in position space at later times. Use your computer to make some graphs that illustrate the behavior of the wave function. (Mathematica can do a nice job with this.) Also, make some graphs that show how the absolute value squared of the wave function varies with time. Set k₀ by setting the classical velocity v₀ = k₀/m to 1 in your computer time units. You should explore how the results depend on the parameters m and a. One good illustrative case is a = 0.1 and m = 100, with x and t in the range -1 < x < 5 and 0 < t < 5. Try also a particle that is classically at rest, v₀ = 0.
7. Wednesday 18 November. Sakurai, problems 2.15 and 2.22, plus exercise 2.1 from the notes Path integrals and the classical approximation.
8. Wednesday 25 November. Derive Eq. (4) (for the propagator of a free particle in three dimensions) in the notes Path integrals and the classical approximation. Derive Eq. (2.6.27) in Sakurai. Do problem 2.36 in Sakurai.
9. Friday 4 December. We will not have problems to hand in, but please work out exercises 3.1, 7.1, and 7.2 in the notes The rotation group and quantum mechanics.
10. Tuesday 8 December. Final exam. In preparation, you might want to look at the final exam from last year.

Available notes in .pdf and .nb format:

• Vectors for quantum mechanics (12 October 2009).
• Choice of units for quantum mechanics (16 October 2009).
• Comments on homework for 14 October. (19 October 2009).
• Position and momentum in quantum mechanics (23 October 2009).
• Comment on Sakurai problem 1.29 (1 November 2009).
• Path integrals and the classical approximation (18 November 2009).
• The rotation group and quantum mechanics (2 December 2009).

Exams:

• Midterm Exam: 13:00 Wednesday 28 October.
• Final Exam: 15:15 Tuesday 8 December.

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.