Asymptotics of eigenvalues of the Schroedinger operator with a strong delta-interaction on a loop

Details Asymptotics of eigenvalues of the Schroedinger operator with a strong delta-interaction on a loop Asymptotics of eigenvalues of the Schroedinger operator with a strong delta-interaction on a loop

2001-03-23

arxiv.org/abs/math-ph/0103029v1

J. Geom. Phys. 41 (2002), 344-358

Physics

Mathematical Physics

amstex, 15 pages

Scientific paper

10.1016/S0393-0440(01)00071-7

In this paper we investigate the operator $H_{\beta}=-\Delta-\beta\delta(\cdot-\Gamma)$ in $L^{2}({\Bbb R}^{2})$, where $\beta>0$ and $\Gamma$ is a closed $C^{4}$ Jordan curve in ${\Bbb R}^{2}$. We obtain the asymptotic form of each eigenvalue of $H_{\beta}$ as $\beta$ tends to infinity. We also get the asymptotic form of the number of negative eigenvalues of $H_{\beta}$ in the strong coupling asymptotic regime.

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