A PT-Invariant Potential With Complex QES Eigenvalues

Abstract

We show that the quasi-exactly solvable eigenvalues of the Schrödinger 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.

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

References in corpus (1)

• A new PT symmetric complex Hamiltonian with a real spectra

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