  We consider the singular semiclassical initial value problem for the phase
space Schrodinger equation. We approximate semiclassical quantum evolution in
phase space by analyzing initial states as superpositions of Gaussian wave
packets and applying individually semiclassical anisotropic Gaussian wave
packet dynamics, which is based on the the nearby orbit approximation; we
accordingly construct a semiclassical approximation of the phase space
propagator, the semiclassical wave packet propagator. By the semiclassical
propagator we construct asymptotic solutions of the phase space Schrodinger
equation, noting the connection of this construction to the initial value
repsresentations.
