Titchmarsh–Weyl theory and its relations to scattering theory: Spectral densities and cross sections; Theory and applications

Abstract

The radial equation (or set of equations) derived in scattering theory is analyzed by means of Titchmarsh–Weyl theory for singular second-order differential equations. In particular we have focused on the spectral density concept and the corresponding relation to the scattering cross section. The method of complex deformations is brought in as a necessary ingredient in the evaluation of the underlying pole strings, which together with the background build up the actual dispersion relation data. The analysis is supported by numerical applications to a centrifugal family of simple potentials.