642:561 Math Physics
Introduction to Quantum Mechanics
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
Quantum Mechanics - Schwabl (recommended)