Correct short time propagator for Feynman path integration by power series expansion in Δt
✍ Scribed by Nancy Makri; William H. Miller
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 539 KB
- Volume
- 151
- Category
- Article
- ISSN
- 0009-2614
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✦ Synopsis
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 Ar. 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 At, explicit expressions being given for the terms of order At-', At', and At'. 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 At) to be a significant improvement over previous ones; inclusion of the third-order term gives considerable additional improvement (i.e. faster convergence).