A PT-Invariant Potential With Complex QES Eigenvalues

Details A PT-Invariant Potential With Complex QES Eigenvalues A PT-Invariant Potential With Complex QES Eigenvalues

2000-06-28

arxiv.org/abs/quant-ph/0006126v1

Phys.Lett. A272 (2000) 53-56

Physics

Quantum Physics

8 pages, Latex, No fig, To appear in PLA(2000)

Scientific paper

10.1016/S0375-9601(00)00409-6

We show that the quasi-exactly solvable eigenvalues of the Schr\"odinger
equation for the PT-invariant potential $V(x) = -(\zeta \cosh 2x -iM)^2$ are
complex conjugate pairs in case the parameter M is an even integer while they
are real in case M is an odd integer. We also show that whereas the PT symmetry
is spontaneously broken in the former case, it is unbroken in the latter case.

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