Physics – Mathematical Physics
Scientific paper
2006-04-06
Physics
Mathematical Physics
39 pages
Scientific paper
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 $\{S_\gT(\gl)\}$ 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.
Behrndt Jussi
Malamud Mark M.
Neidhardt Hagen
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