New quasi-exactly solvable Hermitian as well as non-Hermitian $mathcal{PT}$ -invariant potentials

Pramana

Bhabani Prasad Mandal2¹  Avinash Khare² 

[1] Department of Physics, Banaras Hindu University, Varanasi 221 005, India$$;Institute of Physics, Sachivalaya Marg, Bhubaneswar 751 005, India$$

关键词: Quasi-exactly solvable;    non-Hermitian;    $mathcal{PT}$ symmetry;    Bender and Dunne polynomials.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

We start with quasi-exactly solvable (QES) Hermitian (and hence real) as well as complex $mathcal{PT}$ -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 $mathcal{PT}$ - invariant complex QES periodic potentials. We study in detail the various properties of the corresponding Bender–Dunne polynomials.

【 授权许可】

Unknown