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Integral-free Wigner functions

A. Tegmen
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Abstract

Wigner phase space quasi-probability distribution function is a Fourier transform related to a given quantum mechanical wave function. It is shown that for the wave functions of type $ψ(q)=e^{-aq^2}ϕ(q)$, the Wigner function can be defined in terms of differential operators acting on a given function, independently from the integral formula which appears in the standard definition. Gaussian wave packet, harmonic and singular oscillators are given as the examples.

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A. Tegmen. 2007-02-06. Integral-free Wigner functions. https://doi.org/10.1393/ncb%2Fi2006-10148-0

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