The propagator for the step potential using the path decomposition expansion

TL;DR

This paper derives the propagator for a step potential using path integrals and the Path Decomposition Expansion, providing a direct and rigorous approach to quantum propagators in piecewise potentials.

Contribution

It introduces a novel derivation of the propagator for the step potential utilizing the PDX and lattice path limits, offering a new perspective on quantum propagator calculations.

Findings

Derivation of the propagator using PDX and lattice paths

Provides a rigorous, direct path integral approach

Enhances understanding of quantum dynamics in step potentials

Abstract

We present a direct path integral derivation of the propagator in the presence of a step potential. The derivation makes use of the Path Decomposition Expansion (PDX), and also of the definition of the propagator as a limit of lattice paths.