Monte Carlo path integration for the real time propagator

Abstract
Monte Carlo methods are described for evaluating the Feynman path integral representation of the (real time) propagator (time evolution operator), exp(−iHt/ℏ). The approach is based on the modified Filinov algorithm presented earlier by Makri and Miller [Chem. Phys. Lett. 139, 10 (1987)]. Numerical calculations are presented for time evolution in a symmetric double well potential, as well as in a Morse potential.