# Lie Algebras and Quantum Mechanics

# Lie-Algebren und Quantenmechanik

Lie Algebras and Quantum Mechanics

4 hours/week, 7 ECTS

Sprache/Language: English

Arnold Neumaier

**Zeiten/Time:**

Montag/Monday 12:45-14:15, SR10

Mittwoch/Wednesday 12:45-14:15, SR10

Erstmals am/First lecture: Monday, October 2, 2017

This course discusses quantum mechanics from a mathematical point of
view. The emphasis is on techniques closely related to Lie algebras.

The precise content will depend on the audience and will be determined
during the term. Possible topics include:

Small quantum systems, their Lie algebras and Lie groups
Thermodynamics and statistical mechanics
The Schrödinger equation
Eigenvalues and spectroscopy
Unitary representations of Lie groups
Reproducing kernels and coherent states
Central extensions: spin, metaplectic group
Markov processes and quantum dynamical semigroups
Relativity and representations of the Poincaré group

There will be significant overlap between the material for the course
and the content of my online book

My
theoretical physics FAQ
is a useful source for background information.

Prerequisites: Solid knowledge of linear algebra and multivariate
analysis, rudiments of functional analysis and partial differential
equations. No background in physics or Lie groups is assumed.

Credits are given on the basis of an oral exam after the end of
the course.

## Useful external reading

Quantum Theory, Groups and Representations: An Introduction
by Peter Woit

An Elementary Introduction to Groups and Representations
by Brian C. Hall

Courses

my
home page (http://www.mat.univie.ac.at/~neum/)

Arnold Neumaier (Arnold.Neumaier@univie.ac.at)