Scattering matrices and Dirichlet-to-Neumann maps

Jussi Behrndt*, Mark Malamud, Hagen Neidhardt

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 Schrödinger operators on unbounded domains, Schrödinger operators with singular potentials supported on hypersurfaces, and orthogonal couplings of Schrödinger operators. In these applications the scattering matrix is expressed in an explicit form with the help of Dirichlet-to-Neumann maps.
Original languageEnglish
Pages (from-to)1970 - 2025
JournalJournal of Functional Analysis
Issue number6
Publication statusPublished - 2017


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