MAT265 Homepage

Mathematical Quantum Mechanics, CRN 92912. This class meets on Tuesdays and Thursdays, 10:30-11:50am, in 1038 Wickson Hall.

Instructor: Bruno Nachtergaele
E-mail: bxn@math.ucdavis.edu
Office: 669 Kerr Hall, Phone: (530) 752-8061

Topical Outline: Foundations of quantum mechanics, Hilbert space and operator algebra formulations, Schrödinger and Heisenberg equations, analysis of simple systems, symmetry in quantum mechanics, representations of SU(2) and spin, spectral theory of Schrödinger operators, perturbation theory, applications to atoms and molecules, the Dirac equation.

Textbooks and References:
(GS) S. Gustafson & I.M. Sigal, Mathematical Concepts of Quantum Mechanics, Springer, 2003.
(Sch) J. Schwinger, Quantum Mechanics. Symbolism of Atomic Measurements, Springer 2001, 2003.
(Sak) J.J. Sakurai, Modern Quantum Mechanics, Addison Wesley 1994, revised edition.
(GP) A. Galindo & P. Pascual, Quantum Mechanics I & II, 2nd edition, Springer 1989.
(RS) M. Reed & B. Simon, Methods of Modern Mathematical Physics. I-IV, Academic Press 1980.
(Thi) W. Thirring, Quantum Mathematical Physics, 2nd edition, Springer 2002.
(Kat) T. Kato, Perturbation Theory for Linear Operators, Springer 1980, reprinted 1995.
(BR) O. Bratteli & D.W. Robinson, Operator Algebras and Quantum Statistical Mechanics, volume 1 & 2, 2nd edition, Springer 1987, 1997.

Brief SU(2) notes: SU(2).PDF.

Andrew Waldron, Fiat Lux, notes for his guest lecture on the quantum theory of light.

Office hours:
Fridays 2:00-3:00pm, or by appointment.

Check your email regularly!
I will use email to make announcements (e.g., about homework and exams) and I will often not repeat these announcements in class. All e-mail messages to the class list are collected in a Web Archive . Grade Distribution: Homework 20%, Midterm 30% (take-home), Final 50% (12/11, 10:30-12:30pm, 1038 Wickson). There will be five homework assignments with a choice of problems, of which you will need to pick about five for each homework.

Homework assignments:
HW 1 in PDF format; due on Tuesday, October 14.
HW 2 in PDF format; due on Tuesday, October 28.
HW 3 in PDF format; due on Thursday, November 13.

Midterm Topics:
1. Square well potentials (GP 4.3, GS 7.4).
2. The harmonic oscillator (GP 4.4, GS 7.5).
3. Delta function potentials (GP 4.6).
4. A potential step (GS 7.3, GP 4.5).
5. The Hydrogen atom (GS 7.7, GP 6.5).
6. A particle in a magnetic field (GS 7.8).
7. A particle on a sphere (GS 7.6).
Please email me with your choice. I am also open to your own suggestion, if you have one. Midterm papers are due on Thursday, November 20.

Final Exam:
Take-home final exam assignment, due on Thursday, December 11, 6pm, at my office or in my mailbox.