Weakly Coupled Bound States

Abstract

A situation of separate interest concerns geometric perturbations which are weak. One can then derive useful expansions of such weakly bound states by modifying the classical Birman-Schwinger method. There are also other ways to address this problem. One is using a variational technique, it is illustrated here on waveguides with a small and critical deformation. The other possibility is represented by matching the solutions in different parts of the guide; this method is particularly suitable for waveguides with perturbations situated far from each other.