Isospectral Potentials from Modified Factorization

TL;DR

This paper explores the non-uniqueness of quantum potential factorization to generate new isospectral potentials, providing a systematic method and examples with potential applications in atomic and molecular physics.

Contribution

It introduces a novel method to derive isospectral non-singular potentials using modified factorization involving excited states and superpotentials.

Findings

Multiple one-parameter families of isospectral potentials generated

Operator representations for these potentials are constructed

Method applicable to atomic and molecular physics scenarios

Abstract

Factorization of quantum mechanical potentials has a long history extending back to the earliest days of the subject. In the present paper, the non-uniqueness of the factorization is exploited to derive new isospectral non-singular potentials. Many one-parameter families of potentials can be generated from known potentials using a factorization that involves superpotentials defined in terms of excited states of a potential. For these cases an operator representation is available. If ladder operators are known for the original potential, then a straightforward procedure exists for defining such operators for its isospectral partners. The generality of the method is illustrated with a number of examples which may have many possible applications in atomic and molecular physics.