A PT-Invariant Potential With Complex QES Eigenvalues

الأصل · EN

We show that the quasi-exactly solvable eigenvalues of the Schrödinger equation for the PT-invariant potential V(x) = -(ζ 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.