**COURSE PREFIX/NUMBER:** MAT 494 B
**TITLE OF COURSE:**
*Mathematics of Quantum Mechanics*
**INSTRUCTOR:**
Dr. Sergei K. Suslov
**TIME:**
3:40-4:55, MW
**LOCATION:**
PSA 307
**LINE #**:
69537

**COURSE DESCRIPTION**

The main purpose of this course is to help beginners explore the World
of Quantum

Mechanics, one of the most important scientific discoveries of the
last century, and

a subject that is very important in the education of student majoring
in science or

engineering.

This course uses mathematical methods which are not always part of the

usual course sequence. It is designed as an introduction to quantum
mechanics,

with emphasis on the mathematical aspects of the theory. This includes

the Schrodinger equation, the WKB approximation, angular momentum and
spin,

some applications of the theory of symmetry in quantum mechanics, motion
in a

magnetic field and, if time permits, the Dirac equation and/or other
topics

in relativistic theory.

All mathematical tools (aspects of analytic function theory, orthogonal
polynomials,

special functions, group representations, and asymptotic methods) will
be introduced

as needed.

**PREREQUISITES:** MAT 272 and 342.

**TEXTBOOK:**

A. Messiah, *Quantum Mechanics*, Dover, 2001

or any other similar textbook on non-relativistic quantum mechanics.

**RECOMMENDED SUPPLEMENTARY BOOKS:**

I. I. Gol'dman and V. D. Krivchenkov, *Problems in Quantum Mechanics*,

Dover, New York, 1993;

S. Flugge, *Practical Quantum Mechanics*, Springer, 1999

(reprint of the 1994 edition);

L. D. Landau and E. M. Lifshitz, *Quantum Mechanics*,

Third revised edition 1977, reprinted by Butterworth-Heinemann, 1998;

E. Merzbacher, *Quantum Mechanics*, Wiley, New York, 1998;

A. F. Nikiforov and V. B. Uvarov, *Special Functions of Mathematical
Physics*, Birkhauser, Boston, 1988.

For more information contact Sergei Suslov:
**office: **PSA 643,
**phone #** 965-8987
**e-mail:** sks@asu.edu,
**URL: ** http://hahn.la.asu.edu/~suslov/index.html

**PROJECTS**

1. The WKB approximation. Bohr-Sommerfeld's quantization
rule.

2. Perturbation theory. Perturbations independent of time.
The secular equation.

3. Motion in a Coulomb field (sperical coordinates and
parabolic coordinates).

4. Rotational symmetry: the rotation operator, angular
momentum and conservation laws.

5. The representations of the rotation group.

6. Addition of angular momenta. Clebsch-Gordan coefficients.
Racah coefficients.

7. Irreducible tensor operators.

8. Hidden symmetry of the hydrogen atom.

9. Scattering. The cross section. The Born approximation.

10. Scattering in the Coulomb field.

11. The spin. The spin operator, Pauli matrices and spin angular
momentum.

12. Motion in magnetic field. Schrodinger equation in a magnetic
field.

13. Motion in a uniform magnetic field. Landau levels.

14. A hydrogen atom in an electric field. The Stark effect.

15. The Dirac equation: solutions of the free field Dirac equation.

16. The Dirac equation: central forces and the hydrogen atom.

17. Tree method for multidamensional Laplace equation.

**HOMEWORK PROBLEMS**

Gol'dman and Krivchenkov:

**Section 1**: # 1, 2, 3, 4, 5, 6, 7, 10, 11, 12

**Section 3**: # 1, 2, 3