On the WKB Approximation to the Propagator for Arbitrary Hamiltonians

摘要

The purpose of this paper is to obtain a general expression for the WKB approximation to the propagator corresponding to an arbitrary Hamiltonian operator. In an earlier publication we determined a range of validity of Van Vleck's well-known formula, which was known not to be universally valid. The approximation derived here, generalizing Van Vleck's formula, is also valid beyond quantum-mechanical applications such as the Fokker-Planck equation for diffusion processes. We operate in n dimensions and summation over repeated indices is implied.