Decomposition of the Feynman kernel for a particle in a box

TL;DR

This paper investigates how the phase factor in the Feynman kernel for a particle in a box with a specific potential depends on the potential parameter, extending the understanding beyond the free particle case.

Contribution

It generalizes the phase factor in the Feynman kernel for a particle in a box with a $1/ ext{sin}^2\theta$ potential, showing its dependence on the potential parameter.

Findings

The phase factor $-1$ for free particles is generalized for the potential case.

The decomposition of the Feynman kernel reveals parameter-dependent phase factors.

The results improve the understanding of quantum boundary reflections with potentials.

Abstract

We study the decomposition of the Feynman kernel for a particle in a box with $1/\sin^{2}\theta$ potential to find that the wellknown phase factor $-1$, which is correct for the case of the free particle, for reflection at boundaries should be generalized depending on the parameter of the potential.