The R matrix: Its relation to titchmarsh-Weyl theory and its complex rotated analogue

Abstract

The R matrix theory in its simplest form is discussed and analyzed in terms of the classical Titchmarsh–Weyl's theory for a singular second order differential equation. It is observed that the R matrix described as an abstract R operator is contained in the framework of Weyls classical extension to an infinite interval of finite Sturm–Liuoville theory. As a result we find that the exterior complex rotation method can be synthesized with the R matrix theory to obtain a method for deriving the S matrix poles out in the complex energy or momentum planes.