PT invariant Non-Hermitian Potentials with Real QES Eigenvalues

Avinash Khare; Bhabani Prasad Mandal

PT invariant Non-Hermitian Potentials with Real QES Eigenvalues

量子物理 2007-05-23 v2 高能物理 - 理论数学物理 math.MP

作者: Avinash Khare , Bhabani Prasad Mandal

摘要

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.

关键词

painlevé equations and orthogonal polynomials

引用

@article{arxiv.quant-ph/0004019,
  title  = {PT invariant Non-Hermitian Potentials with Real QES Eigenvalues},
  author = {Avinash Khare and Bhabani Prasad Mandal},
  journal= {arXiv preprint arXiv:quant-ph/0004019},
  year   = {2007}
}

备注

13 pages, Latex, no figs Revised version, Major changes in Title, Abstract, Introduction and Conclusion; Refs added

PT invariant Non-Hermitian Potentials with Real QES Eigenvalues

摘要

关键词

引用

备注

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