Time dependent quantum propagation in phase space

Numerical solutions of the quantum time-dependent integro-differential Schr odinger equation in a coherent state Husimi representation are investigated . Discretization leads to propagation on a grid of nonorthogonal coherent s tates without the need to invert an overlap matrix, with the further advant age of a sparse Hamiltonian matrix. Applications are made to the evolution of a Gaussian wave packet in a Morse potential. Propagation on a static rec tangular grid is fast and accurate. Results are also presented for a moving rectangular grid, guided at its center by a mean classical path, and for a classically guided moving grid of individual coherent states taken from a Monte Carlo ensemble. (C) 2000 American Institute of Physics. [S0021-9606(0 0)00546-8].