Delta potentials revisited via Fourier transform

TL;DR

This paper revisits the quantum bound state problem in delta potentials using Fourier transform methods, simplifying the solution process and avoiding the need for jump discontinuity knowledge.

Contribution

It introduces a Fourier transform approach to solve delta potential problems, simplifying the analysis and extending easily to multiple delta functions.

Findings

Simplified solution for single delta potential bound states.

Extended method to multiple delta potentials.

Avoids need for jump discontinuity knowledge.

Abstract

The problem of bound states in delta potentials is revisited by means of Fourier transform approach. The problem in a simple delta potential sums up to solve an algebraic equation of degree one for the Fourier transform of the eigenfunction and the problem for more than one delta function also reveals itself to be a simple matter. Quite differently from direct methods, no knowledge about the jump discontinuity of the first derivative of the eigenfunction is required to determine the solution of the problem.