On integral and differential representations of Jordan chains and the confluent supersymmetry algorithm

TL;DR

This paper explores the connection between integral and differential forms of Jordan chains, applying it to improve the confluent supersymmetry algorithm and to compute normalization constants in quantum systems with energy-dependent potentials.

Contribution

It establishes a new relationship between integral and differential representations of Jordan chains, enhancing the analysis of supersymmetry transformations and quantum wave functions.

Findings

Derived conditions for regular potentials via the confluent supersymmetry algorithm.

Provided a method to compute normalization constants for energy-dependent quantum potentials.

Expressed integrals involving Schrödinger solutions through derivatives.

Abstract

We construct a relationship between integral and differential representation of second-order Jordan chains. Conditions to obtain regular potentials through the confluent supersymmetry algorithm when working with the differential representation are obtained using this relationship. Furthermore, it is used to find normalization constants of wave functions of quantum systems that feature energy-dependent potentials. Additionally, this relationship is used to express certain integrals involving functions that are solution of Schrodinger equations through derivatives.