Recent progress obtained in semiclassical approximations to the propagator of the Wigner function [Phys. Rev. Lett. 96, 070403 (2006)] indicate that the phase space representations of quantum dynamics is a promising strategy to surmount the long-standing problems of semiclassical propagation. In this work we apply the semiclassical Wigner propagator to the Morse oscillator, a benchmark system for quantum- mechanical propagation in strongly nonlinear potentials. We compare two semiclassical approachs in phase space to the exact quantum solution applied to a coherent state as initial condition. |