Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 4 (2008), 054, 12 pages      arXiv:0807.1966      http://dx.doi.org/10.3842/SIGMA.2008.054

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

Dieter Schuch a and 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

Received February 06, 2008, in final form June 08, 2008; Published online July 14, 2008

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.

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

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