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The propagator for the step potential and delta function potential using the path decomposition expansion
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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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The real-time Feynman path integral for step potentials
Complex semiclassical paths in the Feynman path integral for step potentials can be organized into equivalence classes, and one unsuppressed class provides the instanton mechanism for quantum reflection.
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