On the One-Dimensional Harmonic Oscillator with a Singular Perturbation

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2016Embargo end date: 01 Jan 2015Publisher:FSAEIHE South Ural State University (National Research University)Journal:Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming and Computer Software", volume 9, pages 73-91 (issn: 2071-0216,

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Authors: STRAUSS V.A.; WINKLMEIER M.A.;

doi: 10.14529/mmp160106 , 10.48550/arxiv.1506.06264

arXiv: 1506.06264

On the One-Dimensional Harmonic Oscillator with a Singular Perturbation

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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.

Keywords

HARMONIC OSCILLATOR,SINGULAR PERTURBATION,SELFADJOINT EXTENSIONS,NEGATIVE EIGENVALUES,ГАРМОНИЧЕСКИЙ ОСЦИЛЛЯТОР,СИНГУЛЯРНЫЕ ВОЗМУЩЕНИЯ,САМОСОПРЯЖЕННЫЕ РАСШИРЕНИЯ,ОТРИЦАТЕЛЬНЫЕ СОБСТВЕННЫЕ ЗНАЧЕНИЯ, General theory of ordinary differential operators, Functional Analysis (math.FA), Linear symmetric and selfadjoint operators (unbounded), Mathematics - Functional Analysis, harmonic oscillator, selfadjoint extensions, FOS: Mathematics, 34L40, 81Q10, 81Q15, 35J10, singular perturbation, negative eigenvalues

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