Pavel Exner, Kazushi Yoshitomi
Asymptotics of eigenvalues of the Schroedinger operator
with a strong delta-interaction on a loop
(37K, LaTeX)
ABSTRACT. 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.