Point interactions in a tube (Q2702383)

The author discusses the spectral and scattering properties of a particle in a Dirichlet tube in \(\mathbb{R}^3\) with point interactions. The simplest situation is when the tube is a plane strip [see \textit{P. Exner, R. Gawlista, P. Šeba} and \textit{M. Tater}, Ann. Phys. 252, 133-179 (1996; Zbl 0891.47052)]. NEWLINENEWLINENEWLINEThe current article generalizes those results to a region \(\Omega:= \mathbb{R}\times M\) where \(M\) is a closed compact subset of \(\mathbb{R}^2\) which is pathwise connected and so that \(dM\) has the segment property. Dirichlet boundary conditions are imposed to define the associated Hamiltonian.NEWLINENEWLINEFor the entire collection see [Zbl 0953.00049].