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 ip(q) = e~aq 4>(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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