PT invariant Non-Hermitian Potentials with Real QES Eigenvalues

Details PT invariant Non-Hermitian Potentials with Real QES Eigenvalues PT invariant Non-Hermitian Potentials with Real QES Eigenvalues

2000-04-05

arxiv.org/abs/quant-ph/0004019v2

Physics

Quantum Physics

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

Scientific paper

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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