Abstract
The most commonly used short time propagator in a discretized Feynman path integral (and also several more sophisticated “improved” ones) is not correct through first order in the time increment Δ t. The correct result for the phase (i.e. the action) of the short time propagator is developed in this paper as a power series in Δ t, explicit expressions being given for the terms of order Δ t −1, Δ t, and Δ t 3. Test applications to the standard harmonic oscillator and also to a double well potential (typical for intramolecular H-atom transfer) show the first-order propagator (i.e. the correct result through order Δ t) to be a significant improvement over previous ones; inclusion of the third-order term gives considerable additional improvement (i.e. faster convergence).
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