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

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

2011-12-12

arxiv.org/abs/1112.2545v1

Mathematics

Functional Analysis

22 pages

Scientific paper

We give an abstract definition of a one-dimensional Schr\"odinger operator with $\delta'$-interaction on an arbitrary set~$\Gamma$ 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~$\Gamma$ that have negative values of the intensity constants of the $\delta'$-interaction. In the case where the set~$\Gamma$ is endowed with a Radon measure, we give constructive examples of such operators having an infinite number of negative eigenvalues.

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