Abstract
We start with quasi-exactly solvable (QES) Hermitian (and hence real) as well as complex \( \mathcal{P}\mathcal{T} \)-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 \( \mathcal{P}\mathcal{T} \)-invariant complex QES periodic potentials. We study in detail the various properties of the corresponding Bender-Dunne polynomials.
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Khare, A., Mandal, B.P. New quasi-exactly solvable Hermitian as well as non-Hermitian \( \mathcal{P}\mathcal{T} \)-invariant potentials. Pramana - J Phys 73, 387–395 (2009). https://doi.org/10.1007/s12043-009-0130-8
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DOI: https://doi.org/10.1007/s12043-009-0130-8