  In this work we study the Wigner functions, which are the quantum analogues
of the classical phase space density, and show how a full rigorous
semiclassical scheme for all orders of \hbar can be constructed for them
without referring to the actual coordinate space wavefunctions from which the
Wigner functions are typically calculated. We find such a picture by a careful
analysis around the stationary points of the main quantization equation, and
apply this approach to the harmonic oscillator solving it for all orders of
\hbar.
