Pavel Exner and Sylwia Kondej
Scattering on leaky wires in dimension three
(113K, pdf)
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.