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arXiv · 1112.2545

One-dimensional Schrödinger operators with $δ'$-interactions on a set of Lebesgue measure zero

Johannes F. Brasche·Leonid Nizhnik
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Abstract

We give an abstract definition of a one-dimensional Schrödinger operator with $δ'$-interaction on an arbitrary set~$Γ$ of Lebesgue measure zero. The number of negative eigenvalues of such an operator is at least as large as the number of those isolated points of the set~$Γ$ that have negative values of the intensity constants of the $δ'$-interaction. In the case where the set~$Γ$ is endowed with a Radon measure, we give constructive examples of such operators having an infinite number of negative eigenvalues.

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Johannes F. Brasche, Leonid Nizhnik. 2011-12-12. One-dimensional Schrödinger operators with $δ'$-interactions on a set of Lebesgue measure zero. https://arxiv.org/abs/1112.2545

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