Krein's method in inverse scattering

Abstract

A detailed discussion of the Krein’s results (applicable for solving the inverse scattering problem) is given with complete proofs. It is shown that the S-function S(k) used in Krein’s work is the S-matrix used in physics. The basic new results of the paper include the detailed description and analysis of an inversion algorithm based on Krein’s results and a proof of its consistency, that is the proof that the reconstructed potential generates the same scattering data from which it was reconstructed. Numerical advantages of using Krein’s method are discussed.