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SIGMA 4 (2008), 054, 12 pages arXiv:0807.1966
https://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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