Path Integral Solution of a Class of Explicitly Time-Dependent Potentials

TL;DR

This paper develops a path integral approach to solve a class of explicitly time-dependent potentials, using space-time transformations to compute propagators, with examples demonstrating the method's effectiveness.

Contribution

It introduces a formalism for handling explicitly time-dependent potentials in path integrals via space-time transformations, extending previous methods.

Findings

Derived explicit propagators for specific time-dependent potentials.

Demonstrated the formalism with illustrative examples.

Connected the approach to recent results by Dodonov et al.

Abstract

A specific class of explicitly time-dependent potentials is studied by means of path integrals. For this purpose a general formalism to treat explicitly time-dependent space-time transformations in path integrals is sketched. An explicit time-dependent model under consideration is of the form $V(q,t)=V[q/\zeta(t)]/\zeta^2(t)$, where $V$ is a usual potential, and $\zeta(t)=(at^2+2bt+c)^{1/2}$. A recent result of Dodonov et al.\ for calculating corresponding propagators is incorporated into the path integral formalism by performing a space-time transformation. Some examples illustrate the formalism.