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)