Wigner function 1

$W(x,p):=\frac{1}{\pi \hslash }{\int }_{-\infty }^{\infty }{\varphi }^{\ast }(x+y)\varphi (x-y)\exp \left(\frac{2ipy}{\hslash }\right)dy$. This relates to the moment generating function $\mathbb{E}[e^{tX}]$