Integral-free Wigner functions
Abstract
Description
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.
5 pages, no figures, to appear in "Il Nuovo Cimento B"
5 pages, no figures, to appear in "Il Nuovo Cimento B"