PHYSICS 430

QUANTUM MECHANICS

Catalog Entry

PHYSICS 430. QUANTUM MECHANICS

Credit Hours (3).

Prerequisites: MATH 252, PHYS 112 or 222, and PHYS 305.

An introduction to nonrelativistic quantum mechanics. Topics included are the Schrödinger equation, bound states, angular momentum, spin, scattering theory, and the matrix formulation.

Detailed Description of Course

This course is designed to provide a foundation in nonrelativistic quantum mechanics. The treatment will be elementary but not superficial. The student will be expected to master and apply the mathematical techniques of the subject in certain simplified situations.

The syllabus for the course is:

I. Schrödinger's Equation

a. Introduction

b. The time-dependent Schrödinger equation

c. Interpretation of the wave function

d. The time-independent Schrödinger equation

e. Eigenvalues and eigenvectors

II. Bound State Problems

a. One-dimensional problems: square well, harmonic oscillator

b. Spherically-symmetric potentials in three dimensions; spherical harmonics; angular momentum

c. Three-dimensional square well

d. The hydrogen atom

III. Spin and Symmetry

a. Electron spin; total angular momentum

b. Magnetic moments; Zeeman effect; spin-orbit interaction

c. Identical particles; symmetric and antisymmetric wave functions; the exclusion principle

d. Multi-electron atoms

IV. Scattering Problems

a. One-dimensional problems: step potentials, barrier and square well potentials

b. Collision theory; cross section

c. The Born approximation

d. Partial wave analysis

V. Quantum Mechanical Formalism

a. Operators and matrices

b. Hilbert space

c. Dirac notation

d. Symmetry and conservation laws

Detailed Description of Conduct of Course

The amount of material presented in this course and the formal nature of much of this material requires a heavy dependence on standard lecture presentation. However, as in all physics courses, problem solving will be emphasized, and considerable lecture time will be devoted to problem solving strategies, the presentation of example problems, and the discussion of assigned problems.

Goals and Objectives of the Course

The student learning goals for the course are to be able to state and discuss the basic principles of nonrelativistic quantum mechanics; to be able to analyze basic physical situations in terms of the fundamental theory; and to be able to apply the theory, mathematically and quantitatively, to intermediate-level problems.

Assessment Measures

Student assessment in physics courses is strongly dependent on the evaluation of problem-solving ability. This is true even of the assessment of concept comprehension, since the concepts of physics must ultimately be stated and applied quantitatively. Well-constructed and carefully evaluated problems will reveal whether the student has a misconception at a fundamental level or is having difficulties with the mathematical manipulations in the intermediate steps. Frequent feedback from the instructor is important as the student strives to develop the skills required to solve physics problems at this level. The assessment and feedback should proceed not just through formal tests, although these have their place, but also through classroom presentations. Other feedback could include discussions inside and outside the classroom, one-on-one help sessions between student and instructor, and homework problems.

Other Course Information

None.

Approval and Subsequent Reviews

DATE ACTION REVIEWED BY

September 2001 Reviewed by Walter S. Jaronski, Chair