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

Autor:	Baker, Charles, Mityagin, Boris
Rok vydání:	2019
Předmět:	Mathematics - Spectral Theory Mathematical Physics Mathematics - Classical Analysis and ODEs 34L15 (Primary) 33E30 34L20 34L40 34M30 47B44 47E05 (Secondary)
Zdroj:	J. Math. Phys 61 (2020), art. no. 043505
Druh dokumentu:	Working Paper
DOI:	10.1063/1.5139901
Popis:	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. Comment: 26 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1907.10564 Zobrazit plný text záznamu View this record from Arxiv