On the one-dimensional harmonic oscillator with a singular perturbation

Abstract

In this paper we investigate the one-dimensional harmonic oscillator with a singular perturbation concentrated in one point. We describe all possible selfadjoint realizations and we show that for certain conditions on the perturbation exactly one negative eigenvalues can arise. This eigenvalue tends to $-\infty$ as the perturbation becomes stronger.

References in corpus (1)

• Solution of the quantum harmonic oscillator plus a delta-function potential at the origin: The oddness of its even-parity solutions