  The Husimi distribution provides for a coarse grained representation of the
phase space distribution of a quantum system, which may be used to track the
growth of entropy of the system. We present a general and systematic method of
solving the Husimi equation of motion for an isolated quantum system, and we
construct a coarse grained Hamiltonian whose expectation value is exactly
conserved. As an application, we numerically solve the Husimi equation of
motion for two-dimensional Yang-Mills quantum mechanics (the x-y model) and
calculate the time evolution of the coarse grained entropy of a highly excited
state. We show that the coarse grained entropy saturates to a value that
coincides with the microcanonical entropy corresponding to the energy of the
system.
