2008/04/09 by Jussi Behrndt, Mark M. Malamud, Hagen Neidhardt
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Quantum Mechanics and Non-Hermitian Physics #Advanced Operator Algebra Research
paper · doi:10.1112/plms/pdn016
For a scattering system AΘ, A0 consisting of self-adjoint extensions AΘ and A0 of a symmetric operator A with finite deficiency indices, the scattering matrix SΘ(λ) and a spectral shift function ξΘ are calculated in terms of the Weyl function associated with a 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.