New quasi-exactly solvable Hermitian as well as

non-Hermitian PT-invariant potentials

AVINASH KHARE¹ and BHABANI PRASAD MANDAL^2,*

¹Institute of Physics, Sachivalaya Marg, Bhubaneswar 751 005, India

²Department of Physics, Banaras Hindu University, Varanasi 221 005, India

^*Corresponding author. E-mail: bhabani.mandal@gmail.com

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.

Keywords. Quasi-exactly solvable; non-Hermitian;

PT symmetry; Bender and Dunne polynomials.

PACS Nos 03.65.Ge; 11.30.Er