  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 $\psi (q)=e^{-aq^2}\phi (q)$, 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.
