 02133 Pavel Exner, Sylwia Kondej
 Curvatureinduced bound states for a delta interaction
supported by a curve in $\mathbb{R}^3$
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Mar 18, 02

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Abstract. We study the Laplacian in $L^2(\mathbb{R}^3)$
perturbed on an infinite curve $\Gamma$ by a $\delta$ interaction
defined through boundary conditions which relate the corresponding
generalized boundary values. We show that if $\Gamma$ is smooth
and not a straight line but it is asymptotically straight in a
suitable sense, and if the interaction does not vary along the
curve, the perturbed operator has at least one isolated eigenvalue
below the threshold of the essential spectrum.
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