Hyperconfluent third-order supersymmetric quantum mechanics

TL;DR

This paper explores hyperconfluent third-order supersymmetric quantum mechanics, demonstrating that its potentials can be generated through sequential lower-order SUSY transformations, with applications to free particles and Coulomb potentials.

Contribution

It introduces a method to obtain hyperconfluent third-order SUSY potentials via consecutive second- and first-order transformations with the same factorization energy.

Findings

Potential construction via lower-order SUSY transformations

Application to free particle and Coulomb potential cases

Demonstration of the method's validity

Abstract

The hyperconfluent third-order supersymmetric quantum mechanics, in which all the factorization energies tend to a common value, is analyzed. It will be shown that the final potential as well can be achieved by applying consecutively a confluent second-order and a first-order SUSY transformations, both with the same factorization energy. The technique will be applied to the free particle and the Coulomb potential.