Wigner function and the parity operator

Yue Zhang, Shunlong Luo

V. V. Dodonov

David K. Ferry, Xavier Oriols, Josef Weinbub

Antoine Royer

It is pointed out that the Wigner function $f(r, p)$ is $\frac{2}{h}$ times the expectation value of the parity operator that performs reflections about the phase-space point $r$, $p$. Thus $f(r, p)$ is proportional to the overlap of the wave function $\ensuremath{\psi}$ with its mirror image about $r$, $p$; this is clearly a measure of how much $\ensuremath{\psi}$ is centered about $r$, $p$, and the Wigner distribution function now appears physically more meaningful and natural than it did previously.

Apostol Vourdas

A quantum system with positions in Z p and momenta in Q p /Z p is studied. The displacement operators and also the displaced parity operators in the Z p × Q p /Z p phase space of this system, are studied. The Weyl functions (which are intimately related to the displacement operators) and the Wigner functions (which are intimately related to the displaced parity operators) are discussed.

Sibel Başkal, Young S Kim, Marilyn E. Noz