PT-symmetric eigenvalues for homogeneous potentials

Abstract

We consider one-dimensional Schrödinger equations with homogeneous potential, under appropriate PT-symmetric boundary conditions. We prove the phenomenon which was discovered by Bender and Boettcher by numerical computation: as the degree of the potential changes, the real spectrum suddenly becomes non-real in the sense that all but finitely many eigenvalues become non-real. We find the limit arguments of these non-real eigenvalues as they tend to infinity.

27 pages, 9 figures

References in corpus (2)

• The ODE/IM Correspondence
• Behavior of eigenvalues in a region of broken-PT symmetry

Cited by in corpus (1)

• Non-real eigenvalues of the Harmonic Oscillator perturbed by an odd, two-point $\delta$-potential