dorsal/arxiv
View SchemaPT invariant Non-Hermitian Potentials with Real QES Eigenvalues
| Authors | Avinash Khare, Bhabani Prasad Mandal |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0004019 |
| URL | https://arxiv.org/abs/quant-ph/0004019 |
Abstract
We show that at least the quasi-exactly solvable eigenvalues of the Schr\"odinger equation with the potential $V(x) = -(\zeta \cosh 2x -iM)^2$ as well as the periodic potential $V(x) = (\zeta \cos 2\theta -iM)^2$ 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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"abstract": "We show that at least the quasi-exactly solvable eigenvalues of the\nSchr\\\"odinger equation with the potential $V(x) = -(\\zeta \\cosh 2x -iM)^2$ as\nwell as the periodic potential $V(x) = (\\zeta \\cos 2\\theta -iM)^2$ are real for\nthe PT-invariant non-Hermitian potentials in case the parameter $M$ is any odd\ninteger. We further show that the norm as well as the weight functions for the\ncorresponding weak orthogonal polynomials are also real.",
"arxiv_id": "quant-ph/0004019",
"authors": [
"Avinash Khare",
"Bhabani Prasad Mandal"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"title": "PT invariant Non-Hermitian Potentials with Real QES Eigenvalues",
"url": "https://arxiv.org/abs/quant-ph/0004019"
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