Some spectral equivalences between Schrodinger operators

TL;DR

This paper establishes spectral equivalences between different classes of Schrödinger operators, including PT-symmetric and Hermitian problems, using Bethe ansatz equations, leading to isospectrality in some cases.

Contribution

It introduces a method to identify spectral equivalences between Schrödinger operators, extending to full isospectrality and connecting PT-symmetric with Hermitian problems.

Findings

Spectral equivalences of quasi-exactly solvable sectors are established.

Full isospectrality can be achieved in some cases.

Connections between PT-symmetric and Hermitian operators are demonstrated.

Abstract

Spectral equivalences of the quasi-exactly solvable sectors of two classes of Schrodinger operators are established, using Gaudin-type Bethe ansatz equations. In some instances the results can be extended leading to full isospectrality. In this manner we obtain equivalences between PT-symmetric problems and Hermitian problems. We also find equivalences between some classes of Hermitian operators.