Scattering matrices and Weyl functions
Jussi Behrndt, Mark M. Malamud, Hagen Neidhardt
Abstract
For a scattering system \AΘ,A0\ consisting of selfadjoint extensions AΘ and A0 of a symmetric operator A with finite deficiency indices, the scattering matrix \S()\ and a spectral shift function ξΘ are calculated in terms of the Weyl function associated with the boundary triplet for A* and a simple proof of the Krein-Birman formula is given. The results are applied to singular Sturm-Liouville operators with scalar and matrix potentials, to Dirac operators and to Schrödinger operators with point interactions.
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