Dieter Schuch, Marcos Moshinsky, “Wigner Distribution Functions and the Representation of Canonical Transformations in Time-Dependent Quantum Mechanics”, SIGMA, 2008, Volume 4,054, 12 pp.

This article is cited in 11 papers

Wigner Distribution Functions and the Representation of Canonical Transformations in Time-Dependent Quantum Mechanics

Dieter Schuch^a, Marcos Moshinsky^b

^a Institut für Theoretische Physik, Goethe-Universität Frankfurt am Main, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main, Germany
^b Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 México D.F., México

Abstract: For classical canonical transformations, one can, using the Wigner transformation, pass from their representation in Hilbert space to a kernel in phase space. In this paper it will be discussed how the time-dependence of the uncertainties of the corresponding time-dependent quantum problems can be incorporated into this formalism.

Keywords: canonical transformations; Wigner function; time-dependent quantum mechanics; quantum uncertainties.

MSC: 37J15; 81Q05; 81R05; 81S30

Received: February 6, 2008; in final form June 8, 2008; Published online July 14, 2008

Language: English

DOI: 10.3842/SIGMA.2008.054