New QES Hermitian as well as non-Hermitian PT invariant Potentials

TL;DR

This paper explores the construction of new quasi-exactly solvable potentials, both Hermitian and PT-invariant, including complex and periodic cases, and analyzes their properties through polynomial methods.

Contribution

It introduces novel QES potentials derived from known models using perturbations and anti-isospectral transformations, expanding the class of solvable quantum systems.

Findings

QES potentials remain solvable after perturbations

Construction of complex PT-invariant QES periodic potentials

Analysis of Bender-Dunne polynomials for these potentials

Abstract

We start with quasi-exactly solvable (QES) Hermitian (and hence real) as well as complex PT-invariant, double sinh-Gordon potential and show that even after adding perturbation terms, the resulting potentials, in both cases, are still QES potentials. Further, by using anti-isospectral transformations, we obtain Hermitian as well as PT-invariant complex QES periodic potentials. We study in detail the various properties of the corresponding Bender-Dunne polynomials.