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Journal of Mathematical Physics / Volume 24 / Issue 1

J. Math. Phys. 24, 97 (1983); http://dx.doi.org/10.1063/1.525607 (4 pages)

When is the Wigner function of multidimensional systems nonnegative?

Francisco Soto and Pierre Claverie

Laboratoire de Chimie Quantique, Institut de Biologie Physico‐Chimique, 13, rue Pierre et Marie Curie, 75005 Paris, France

(Received 24 February 1981; accepted 18 September 1981)

It is shown that, for systems with an arbitrary number of degrees of freedom, a necessary and sufficient condition for the Wigner function to be nonnegative is that the corresponding state wavefunction is the exponential of a quadratic form. This result generalizes the one obtained by Hudson [Rep. Math. Phys. 6, 249 (1974)] for one‐dimensional systems.

KEYWORDS and PACS

Keywords

one−dimensional systems, wave functions, wigner theory, probability, distribution, space, gauss function, many−dimensional calculations

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.525607

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

For access to fully linked references, you need to log in.
    E. Wigner, Phys. Rev. 40, 749–759 (1932).

    R. J. Glauber, Phys. Rev. 131, 2766–2788 (1963).

    J. C. T. Pool, J. Math. Phys. 7, 66–76 (1966JMAPAQ000007000001000066000001).


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