Integral-free Wigner functions

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 $\psi (q)=e^{-a{q}^2}\varphi (q)$, 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.

5 pages, no figures, to appear in "Il Nuovo Cimento B"