Guiding paths and time-dependent basis sets for wavefunction propagation

Two methods are explored for evolving wavefunctions using short-time propagators of Herman–Kluk form [M.F. Herman, E.K. Kluk, Chem. Phys. 91 (1984) 271]. At each time step the wavefunction is expanded in a set of coherent states distributed in phase space about a guiding trajectory. A harmonic approximation for the potential allows the stability analysis to be done analytically. A Monte Carlo `path integralʹ form for the long-time propagator is derived and tested for a simple harmonic system. Another approach, where the entire wavefunction is evolved one step at time, is applied to wavepacket motion in a Morse potential.