PHYS 631
Quantum Mechanics

Fall Quarter 2008

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 Friday 17 October, so there will be no class that day.
• There will be a makeup class on Friday 24 October from 14:00 to 14:50.
• I will be out of town on Friday 21 November and Friday 5 December, so there will be no class on those days. We will have an extended makeup class on Wednesday 3 December from 6:30 pm to 8:30 pm at a location to be announced.

Reading:

• 29 Sep - 3 Oct: Secs. 1.1 through 1.4.
• 6 Oct - 10 Oct: Secs. 1.5 through 1.6.
• 13 Oct - 17 Oct: Sec. 1.7.
• 20 Oct - 24 Oct: Sec. 2.1 through 2.3.
• 27 Oct - 30 Oct: Sec. 2.4.
• 3 Nov - 7 Nov: Sec. 2.5.
• 10 Nov - 14 Nov: continue with Sec. 2.5.
• 17 Nov - 21 Nov: Sec. 2.6.
• 24 Nov - 26 Nov: continue with Sec. 2.6.
• 1 Dec - 5 Dec: Secs. 3.1-3.3.

Homework:

1. Monday 6 October. Exercises 1.1, 1.2, 1.3 and 1.4 in my notes Vectors for quantum mechanics.
2. Monday 13 October. Sakurai, problems 2, 6, 19, and 23 at end of Chapter 1.
3. Monday 20 October. Sakurai, problems 29, 32, and 33 at end of Chapter 1.
4. Monday 27 October. Sakurai, problems 1, 7, and 8 at end of Chapter 2.
5. Monday 3 November. Suppose that a particle is described at time zero by the gaussian wave function in momentum space in Sakurai Eq. (1.7.42). The particle evolves according to the free hamiltonian p²/(2m). Find the wave function in position space at later times. Make some graphs that illustrate the behavior of the wave function. Also, make some graphs that show how the absolute value squared of the wave function varies with time.
6. Monday 10 November. These problems about a particle in a square well potential.
7. Monday 17 November. Sakurai, problems 15 and 22 at end of Chapter 2 plus exercise 2.1 in the notes Path integrals and the classical approximation.
8. Monday 24 November. 1) Derive Eq. (2.6.27) in Sakurai. 2) Do problem 36 at end of Chapter 2 of Sakurai.
9. Friday 5 December. Sakurai, problems 1 and 2 at end of Chapter 3. Note that there are *no* problems for Monday 1 December and that these two problems are due on Friday. Since there will be no class on Friday, you can put them in my mailbox at ITS.

Available notes in .pdf and .nb format:

• Vectors for quantum mechanics (13 October 2008).
• Path integrals and the classical approximation (17 November 2008).

Exams:

• Midterm Exam: Monday 3 November.
• Final Exam: 15:15 Wednesday 10 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.