Isospectrality of conventional and new extended potentials, second-order supersymmetry and role of PT symmetry

TL;DR

This paper introduces a systematic method for constructing new exactly solvable rational potentials in quantum mechanics, leveraging second-order supersymmetry and PT symmetry to ensure they are free of singularities and isospectral to known systems.

Contribution

It presents a novel approach combining second-order supersymmetry and PT symmetry to generate singularity-free rational potentials that are isospectral to established quantum systems.

Findings

Constructed new rational potentials using second-order supersymmetry.

Demonstrated the role of PT symmetry in avoiding singularities.

Provided examples of the extended potentials and their spectral properties.

Abstract

We develop a systematic approach to construct novel completely solvable rational potentials. Second-order supersymmetric quantum mechanics dictates the latter to be isospectral to some well-studied quantum systems. $\cal PT$ symmetry may facilitate reconciling our approach to the requirement that the rationally-extended potentials be singularity free. Some examples are shown.