New quasi-exactly solvable Hermitian as well as non-Hermitian $$
\mathcal{P}\mathcal{T}
$$-invariant potentials |
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Authors: | Avinash Khare and Bhabani Prasad Mandal |
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Institution: | 1.Sachivalaya Marg,Institute of Physics,Bhubaneswar,India;2.Department of Physics,Banaras Hindu University,Varanasi,India |
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Abstract: | We start with quasi-exactly solvable (QES) Hermitian (and hence real) as well as complex $
\mathcal{P}\mathcal{T}
$
\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}
$
\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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Keywords: | |
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