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

Abstract

In this paper, we consider the perturbations of the Harmonic Oscillator Operator by an odd pair of point interactions: $z(\delta (x-b)-\delta (x+b))$. We study the spectrum by analyzing a convenient formula for the eigenvalue. We conclude that if $z=ir$, $r$ real, as $r\to \infty$, the number of non-real eigenvalues tends to infinity.

26 pages, 2 figures

References in corpus (3)

• The spectrum of a Harmonic Oscillator Operator Perturbed by Point Interactions
• PT-symmetric eigenvalues for homogeneous potentials
• Localization of eigenvalues of Doubly Cyclic Matrices