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| related topics |
| {equation, function, exp} |
| {operator, operators, space} |
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| {let, theorem, proof} |
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PT invariant Non-Hermitian Potentials with Real QES Eigenvalues
Avinash Khare, Bhabani Prasad Mandal
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0004019
- categories:
- quant-ph hep-th math-ph math.MP
- comments:
- 13 pages, Latex, no figs Revised version, Major changes in Title,
Abstract, Introduction and Conclusion; Refs added
- arxiv_id:
- quant-ph/0004019
- created:
- 2000-04-05
- updated:
- 2000-07-06
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