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Scattering matrices and Weyl functions

Jussi Behrndt·Mark M. Malamud·Hagen Neidhardt
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Abstract

For a scattering system $\{A_Θ,A_0\}$ consisting of selfadjoint extensions $A_Θ$ and $A_0$ of a symmetric operator $A$ with finite deficiency indices, the scattering matrix $\{S_\gT(\gl)\}$ and a spectral shift function $ξ_Θ$ 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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Jussi Behrndt, Mark M. Malamud, Hagen Neidhardt. 2006-04-06. Scattering matrices and Weyl functions. https://doi.org/10.1112/plms%2Fpdn016

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