  The Wigner function is a quantum analogue of the classical joined
distribution of position and momentum. As such is should be a good tool to
study quantum-classical correspondence. In this paper, the classical limit of
the Wigner function is shown using the quantum harmonic oscillator as an
example. The Wigner function is found exactly for all states. The
semi-classical wavefunctions for highly excited states are used as the approach
to the classical limit. Therefore, one can found the classical limit of the
Wigner function for highly excited states and shown that it gives the classical
microcanonical ensemble.
