Multiple parameter structure of Mielnik's isospectrality in unbroken SUSYQM

TL;DR

This paper extends Mielnik's isospectral method in unbroken SUSYQM by introducing an iterative approach that incorporates normalization conditions, resulting in a multi-parameter family of potentials and zero modes.

Contribution

It provides a novel iterative generalization of Mielnik's method, revealing a multiple-parameter structure for zero modes and potentials in unbroken SUSYQM.

Findings

Developed an iterative scheme for Mielnik's isospectral potentials.

Established a multi-parameter family of solutions.

Ensured normalization at each iterative step.

Abstract

Within unbroken SUSYQM and for zero factorization energy, I present an iterative generalization of Mielnik's isospectral method by employing a Schroedinger true zero mode in the first-step general Riccati solution and imposing the physical condition of normalization at each iterative step. This procedure leads to a well-defined multiple-parameter structure within Mielnik's construction for both zero modes and potentials