Operator method for finding new propagators from old

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Abstract
A new approach to finding the exact Green’s function to the time-dependent Schrödinger equation is described. The approach is conceptually simple: one seeks an operator which when commuted through the Schrödinger operator transforms it into the Schrödinger 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.