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PT invariant Non-Hermitian Potentials with Real QES Eigenvalues

Avinash Khare·Bhabani Prasad Mandal
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Abstract

We show that at least the quasi-exactly solvable eigenvalues of the Schrödinger equation with the potential $V(x) = -(ζ\cosh 2x -iM)^2$ as well as the periodic potential $V(x) = (ζ\cos 2θ-iM)^2$ are real for the PT-invariant non-Hermitian potentials in case the parameter $M$ is any odd integer. We further show that the norm as well as the weight functions for the corresponding weak orthogonal polynomials are also real.

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Avinash Khare, Bhabani Prasad Mandal. 2000-07-06. PT invariant Non-Hermitian Potentials with Real QES Eigenvalues. https://arxiv.org/abs/quant-ph/0004019

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