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arXiv · 0712.0313

Hiatus perturbation for a singular Schr\"odinger operator with an interaction supported by a curve in \mathbb{R}^3

Pavel Exner·Sylwia Kondej
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Abstract

We consider Schr\"odinger operators in $L^2(\mathbb{R}^3)$ with a singular interaction supported by a finite curve $\Gamma$. We present a proper definition of the operators and study their properties, in particular, we show that the discrete spectrum can be empty if $\Gamma$ is short enough. If it is not the case, we investigate properties of the eigenvalues in the situation when the curve has a hiatus of length $2\epsilon$. We derive an asymptotic expansion with the leading term which a multiple of $\epsilon \ln\epsilon$.

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Pavel Exner, Sylwia Kondej. 2007-12-03. Hiatus perturbation for a singular Schr\"odinger operator with an interaction supported by a curve in \mathbb{R}^3. https://doi.org/10.1063/1.2845419

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