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arXiv · 1404.1764

Schr\"odinger operators with $\delta$-interactions supported on conical surfaces

Jussi Behrndt·Pavel Exner·Vladimir Lotoreichik
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Abstract

We investigate the spectral properties of self-adjoint Schr\"odinger operators with attractive $\delta$-interactions of constant strength $\alpha > 0$ supported on conical surfaces in ${\mathbb R}^3$. It is shown that the essential spectrum is given by $[-\alpha^2/4,+\infty)$ and that the discrete spectrum is infinite and accumulates to $-\alpha^2/4$. Furthermore, an asymptotic estimate of these eigenvalues is obtained.

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Jussi Behrndt, Pavel Exner, Vladimir Lotoreichik. 2014-04-07. Schr\"odinger operators with $\delta$-interactions supported on conical surfaces. https://doi.org/10.1088/1751-8113%2F47%2F35%2F355202

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