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

Charles Baker; Boris Mityagin

doi:10.1063/1.5139901

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

Spectral Theory 2021-05-17 v1 Mathematical Physics Classical Analysis and ODEs math.MP

Authors: Charles Baker , Boris Mityagin

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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.

Keywords

harmonic oscillator point interactions delta potential non-real eigenvalues spectral perturbation polya urn

Cite

@article{arxiv.1907.10564,
  title  = {Non-real eigenvalues of the Harmonic Oscillator perturbed by an odd, two-point $\delta$-potential},
  author = {Charles Baker and Boris Mityagin},
  journal= {arXiv preprint arXiv:1907.10564},
  year   = {2021}
}

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26 pages, 2 figures

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

Abstract

Keywords

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