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arXiv · 1907.10564

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

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: $z (δ(x - b) - δ(x + b))$. 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.

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Charles Baker, Boris Mityagin. 2019-07-24. Non-real eigenvalues of the Harmonic Oscillator perturbed by an odd, two-point $δ$-potential. https://doi.org/10.1063/1.5139901

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