On the one-dimensional harmonic oscillator with a singular perturbation

2015/06/20 by Vladimir Strauss, Strauss, Vladimir, Monika Winklmeier +1
Mathematics · #34L40 #35J10 #81Q10 #81Q15 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:34L40 #msc:35J10 #msc:81Q10 #msc:81Q15

paper · pdf · doi:10.48550/arxiv.1506.06264

arxiv created 2015/06/20 · arxiv updated 2015/06/23

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 -∞ as the perturbation becomes stronger.

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