Evaluation of inverse integral transforms for undergraduate physics students

TL;DR

This paper introduces a straightforward method for evaluating inverse integral transforms suitable for undergraduate physics students, avoiding complex analysis and using differential equations, with applications in physics.

Contribution

It presents a novel approach to inverse transforms that simplifies the process and broadens educational tools without relying on tables or advanced complex analysis.

Findings

Method successfully evaluates transforms without tables

Approach applies to quantum, semi-classical, and nuclear physics

Provides series representations involving Dirac delta functions

Abstract

We provide a simple approach for the evaluation of inverse integral transforms that does not require any knowledge of complex analysis. The central idea behind the method is to reduce the inverse transform to the solution of an ordinary differential equation. We illustrate the utility of the approach by providing examples of the evaluation of transforms, without the use of tables. We also demonstrate how the method may be used to obtain a general representation of a function in the form of a series involving the Dirac-delta distribution and its derivatives, which has applications in quantum mechanics, semi-classical, and nuclear physics.