On Eisenbudʹs and Wignerʹs R-matrix: A general approach

The main objective of this paper is to give a rigorous treatment of Wignerʹs and Eisenbudʹs 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.