Denis Borisov, Pavel Exner, Rustem Gadyl'shin Geometric coupling thresholds in a two-dimensional strip (56K, LaTeX) ABSTRACT. We consider the Laplacian in a strip $\mathbb{R}\times (0,d)$ with the boundary condition which is Dirichlet except at the segment of a length $2a$ of one of the boundaries where it is switched to Neumann. This operator is known to have a non-empty and simple discrete spectrum for any $a>0$. There is a sequence $0