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Scattering matrices and Weyl functions

2006/04/06 by Jussi Behrndt, Mark M. Malamud, Hagen Neidhardt · 47 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Dirac (video compression format) #Dirac operator #Matrix (chemical analysis) #Operator (biology) #Operator theory #Quantum Mechanics and Non-Hermitian Physics #Scalar (mathematics) #Scattering #Scattering theory #Simple (philosophy) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:47A40 #msc:47A55 #msc:47B25 #msc:47B44 #msc:47E05

paper · pdf · doi:10.1112/plms/pdn016

published in Proceedings of the London Mathematical Society 97(3), 568-598 (Wiley) · 39 pages

arxiv created 2006/04/06 · openalex publication_date 2008/04/09 · arxiv updated 2014/02/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

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.

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