Analytical Properties of S Matrix and Uniqueness of the Scattering Potential

Publisher Website
Google Scholar
Abstract
The Schrödinger equation with the complex momentum k leads to an S matrix with very simple analytical properties. It differs from the conventional S matrix as little as one wishes on the real k axis, but it has, in general, completely different analytical behavior outside the real axis. The present formulation removes some of the unsatisfactory features of the conventional formalism in the sense that no redundant poles can occur and a phase shift determines the scattering potential uniquely. The complete analytical behavior of the S matrix, in particular at infinity, is discussed and the theory is extended to Klein-Gordon and Dirac equations with central potential.