Jussi Behrndt, Mark M. Malamud, Hagen Neidhardt
Published 2015-11-07Version 1
A general representation formula for the scattering matrix of a scattering system consisting of two selfadjoint operators in terms of an abstract operator valued Titchmarsh-Weyl $m$-function is proved. This result is applicable to scattering problems for different selfadjoint realizations of Schr\"odinger operators on unbounded domains, and Schr\"odinger operators with singular potentials supported on hypersurfaces. In both applications the scattering matrix is expressed in an explicit form with the help of Dirichlet-to-Neumann maps.
Remarks on scattering matrices for Schrödiner operators with critically long-range perturbations
Poles and zeros of the scattering matrix associated to defect modes
Hermitian symplectic geometry and the factorisation of the scattering matrix on graphs
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