18-108 Pavel Exner and Sylwia Kondej

Scattering on leaky wires in dimension three (113K, pdf) Nov 13, 18

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Abstract. We consider the scattering problem for a class of strongly singular Schr\"odinger operators in $L^2(\mathbb{R}R^3)$ which can be formally written as $H_{lpha,\Gamma}= -\Delta + \delta_lpha(x-\Gamma)$ where $lpha\in\mathbb{R}$ is the coupling parameter and $\Gamma$ is an infinite curve which is a local smooth deformation of a straight line $\Sigma\subset\mathbb{R}^3$. Using Kato-Birman method we prove that the wave operators $\Omega_\pm(H_{lpha,\Gamma}, H_{lpha,\Sigma})$ exist and are complete.

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