Computation of determinants using contour integrals

TL;DR

This paper presents a method to compute the pre-exponential factor of the Feynman propagator for various potentials using contour integrals, relevant for tunnelling in quantum physics, accessible to advanced undergraduates.

Contribution

It introduces a contour integral approach to calculate the pre-exponential factor in quantum propagators, simplifying the process for a broad class of potentials.

Findings

Contour integrals effectively compute the pre-exponential factor.

Method applicable to a large class of potentials.

Accessible to students with basic differential equations and complex analysis.

Abstract

It is shown how the pre-exponential factor of the Feynman propagator for a large class of potentials can be computed using contour integrals. This is of direct relevance in the context of tunnelling processes in quantum theories. The prerequisites for this analysis are accessible to advanced undergraduate students and involve only introductory courses in ordinary differential equations and complex variables.