 02461 Pavel Exner and Sylwia Kondej
 Bound states due to a strong $\delta$ interaction
supported by a curved surface
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Nov 14, 02

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Abstract. We study the Schr\"odinger operator
$\Delta \alpha \delta (x\Gamma )$ in $L^2(\R^3)$ with a
$\delta$ interaction supported by an infinite nonplanar surface
$\Gamma$ which is smooth, admits a global normal parameterization
with a uniformly elliptic metric. We show that if $\Gamma $
is asymptotically planar in a suitable sense and $\alpha>0$ is
sufficiently large this operator has a nonempty discrete
spectrum and derive an asymptotic expansion of the eigenvalues in
terms of a ``twodimensional'' comparison operator determined by
the geometry of the surface $\Gamma$. [A revised version, to
appear in J. Phys. A]
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