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Non-positivity of the Wigner function and bounds on associated integrals

A. J. Bracken·D. Ellinas·J. G. Wood
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Abstract

The Wigner function shares several properties with classical distribution functions on phase space, but is not positive-definite. The integral of the Wigner function over a given region of phase space can therefore lie outside the interval [0,1]. The problem of finding best-possible upper and lower bounds for a given region is the problem of finding the greatest and least eigenvalues of an associated Hermitian operator. Exactly solvable examples are described, and possible extensions are indicated.

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A. J. Bracken, D. Ellinas, J. G. Wood. 2003-04-16. Non-positivity of the Wigner function and bounds on associated integrals. https://doi.org/10.1556/aph.20.2004.1-2.24

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