Pavel Exner and Konstantin Pankrashkin
Strong coupling asymptotics for a singular Schroedinger operator with an interaction supported by an open arc
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ABSTRACT. We consider a singular Schr\"odinger operator in $L^2(\RR^2)$ written formally as
$-\Delta - eta\delta(x-\gamma)$ where $\gamma$ is a $C^4$ smooth open arc in $\RR^2$ of length $L$ with regular ends. It is shown that the $j$th negative eigenvalue of this operator behaves in the strong-coupling limit, $eta o +\infty$, asymptotically as
\[
E_j(eta)=-rac{eta^2}{4} +\mu_j +