Jussi Behrndt, Mark M. Malamud, Hagen Neidhardt
Published 2006-04-06Version 1
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.
Trace formulae for dissipative and coupled scattering systems
Finite Rank Perturbations, Scattering Matrices and Inverse Problems
A lower Wegner estimate and bounds on the spectral shift function for continuum random Schrödinger operators
