Scattering matrices and Dirichlet-to-Neumann maps

摘要

A general representation formula for the scattering matrix of a scattering system consisting of two self-adjoint operators in terms of an abstract operator valued Titchmarsh-Weyl m-function is proved. This result is applied to scattering problems for different self-adjoint realizations of Schrodinger operators on unbounded domains, Schrodinger operators with singular potentials supported on hypersurfaces, and orthogonal couplings of Schrodinger operators. In these applications the scattering matrix is expressed in an explicit form with the help of Dirichlet-to-Neumann maps. (C) 2017 The Author(s). Published by Elsevier Inc.