2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/90408A 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.LaTeX (amsmath, amsextra) 16 pages, appendix (fixing LaTex idiosincrasies); fixing some minor typosQuantum Physicstext