WIAS Preprint No. 1204, (2007)

On Eisenbud's and Wigner's R-matrix: A general approach



Authors

  • Behrndt, Jussi
  • Neidhardt, Hagen
  • Racec, Roxana
  • Racec, Paul N.
  • Wulf, Ulrich

2010 Mathematics Subject Classification

  • 47A40 34L25 81U20

Keywords

  • Scattering, scattering matrix, R-matrix, symmetric and selfadjoint operators, extension theory, boundary triplets, Weyl function, ordinary differential operators

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.

Appeared in

  • J. Differential Equations, 244 (2008) pp. 2545--2577.

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