The propagator for the step potential and delta function potential using the path decomposition expansion

Details The propagator for the step potential and delta function potential using the path decomposition expansion The propagator for the step potential and delta function potential using the path decomposition expansion

2008-04-15

arxiv.org/abs/0804.2391v1

J. Phys. A 41, 285301 (2008)

Physics

Quantum Physics

11 pages, 3 figures

Scientific paper

10.1088/1751-8113/41/28/285301

We present a derivation of the propagator for a particle in the presence of the step and delta function potentials. These propagators are known, but we present a direct path integral derivation, based on the path decomposition expansion and the Brownian motion definition of the path integral. The derivation exploits properties of the Catalan numbers, which enumerate certain classes of lattice paths.

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