On the One-Dimensional Harmonic Oscillator with a Singular Perturbation | Zendy

Vladimir Strauss | Zendy; Monika Winklmeier | Zendy

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On the One-Dimensional Harmonic Oscillator with a Singular Perturbation

Author(s) -

Vladimir Strauss,

Monika Winklmeier

Publication year - 2016

Publication title -

bulletin of the south ural state university series mathematical modelling programming and computer software

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.338

H-Index - 11

eISSN - 2308-0256

pISSN - 2071-0216

DOI - 10.14529/mmp160106

Subject(s) - harmonic oscillator , perturbation (astronomy) , mathematics , mathematical analysis , anharmonicity , physics , geometry , classical mechanics , mathematical physics , quantum mechanics

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.

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