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 and J.G. Wood, Group Theory and Quasiprobability Integrals of Wigner Functions, submitted.
A.J. Bracken, D. Ellinas and J.G. Wood, in preparation.
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Bracken, A.J., Ellinas, D. & Wood, J.G. Non-positivity of the Wigner function and bounds on associated integrals. Acta Phys. Hung. B 20, 121–124 (2004). https://doi.org/10.1556/APH.20.2004.1-2.24
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DOI: https://doi.org/10.1556/APH.20.2004.1-2.24