06-109 Jussi Behrndt, Mark M. Malamud, Hagen Neidhardt
Scattering matrices and Weyl functions (486K, pdf) Apr 7, 06
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Abstract. For a scattering system $\{A_\Theta,A_0\}$ consisting of selfadjoint extensions $A_\Theta$ and $A_0$ of a symmetric operator $A$ with finite deficiency indices, the scattering matrix $\{S_\Theta(\gl)\}$ and a spectral shift function $\xi_\Theta$ 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 Schr\"odinger operators with point interactions.

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