Integral-free Wigner functions

Details Integral-free Wigner functions Integral-free Wigner functions

2007-02-06

arxiv.org/abs/math-ph/0702018v1

Nuovo Cimento B, 121(9), 937-942 (2006)

Physics

Mathematical Physics

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

Scientific paper

10.1393/ncb/i2006-10148-0

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.

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