Operator method for finding new propagators from old.

Abstract

A new approach to finding the exact Green's function to the time-dependent Schr\"odinger equation is described. The approach is conceptually simple: one seeks an operator which when commuted through the Schr\"odinger operator transforms it into the Schr\"odinger operator of a soluble problem. This approach provides an alternative to both the eigenfunction expansion of the propagator and the path integral. The first example of an exact propagator represented as a ``sum over classical paths'' which is not equal to the Gaussian approximation of the path integral is found.