  A general canonical transformation of mechanical operators of position and
momentum is considered. It is shown that it automatically generates a parameter
s which leads to a generalized (or s-parameterized) Wigner function. This
allows one to derive a generalized (s-parameterized) Moyal brackets for any
dimensions. In the classical limit the s-parameterized Wigner averages of the
momentum and its square yield the respective classical values. Interestingly
enough,in the latter case the classical Hamilton-Jacobi equation emerges as a
consequence of such a transition only if there is a non-zero parameter s.

Quantum Physics