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On Eisenbud's and Wigner's R-matrix: A general approach |
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| Authors: | Jussi Behrndt Hagen Neidhardt Paul N Racec Ulrich Wulf |
| Institution: | a Technische Universität Berlin, Institut für Mathematik, MA 6-4, Straße des 17. Juni 136, D-10623 Berlin, Germany b Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstr. 39, D-10117 Berlin, Germany c Technische Universität Cottbus, Fakultät 1, Postfach 101344, D-03013 Cottbus, Germany d Faculty of Physics, University of Bucharest, PO Box MG-11, 077125 Bucharest Magurele, Romania e National Institute of Materials Physics, PO Box MG-7, 077125 Bucharest Magurele, Romania |
| Abstract: | The main objective of this paper is to give a rigorous treatment of Wigner's and Eisenbud's R-matrix method for scattering matrices of scattering systems consisting of two selfadjoint extensions of the same symmetric operator with finite deficiency indices. In the framework of boundary triplets and associated Weyl functions an abstract generalization of the R-matrix method is developed and the results are applied to Schrödinger operators on the real axis. |
| Keywords: | Scattering Scattering matrix R-matrix Symmetric and selfadjoint operators Extension theory Boundary triplet Weyl function Ordinary differential operators |
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