642:561 Math Physics
Fall 2001
Introduction to Quantum Mechanics
Avy Soffer

This course is an introduction to basic quantum mechanics and its mathematical analysis.
Quantum mechanics was first developed when experiments indicated that particles behave as waves and waves behave well ... as particles.
The resulting theory is fundamental to our understanding and description of the physical reality. Quantum theory had profound implications to virtually all sciences, basic and applied; it opened new directions for research in many mathematical fields, from algebra to analysis. It poses a challenge to our understanding of basic notions like information, randomness, computation and recently led to the new field of quantum computation encryption and teleportation.

Topics include: The physical basis of Q.M., basic postulates, Hilbert spaces and linear operators, square well potentials, point and continuous spectrum, hydrogen atom, harmonic oscillator, path integrals, gauge invariance, self-adjointness, symmetries, 1 qubit computer, 2 qubit systems, Approximation methods: bound states, scattering states.

Prerequisites: Real analysis, Linear algebra


Quantum Mechanics I - A. Galindo, P. Pascual

Functional Analysis - Reed Simon I (recommended)

Hilbert space operators in Q. physics - Blank, Exner, Havlicek (recommended)

Quantum Mechanics - Schwabl (recommended)