Derivative Matrix and Scattering Matrix

Abstract

R.Kronig [1] was the first to point out, on the basis of his and Kramers’ [2] work, that the principle of causality must entail some properties of the collision and scattering matrices. Starting from Kronig’s suggestion, Schutzer and Tiomno [3] gave, for non relativistic particles, a derivation of the well known theorem [4] that the poles of the scattering function S(k) lie either in the lower half plane or on the imaginary axis of k. Schutzer and Tiomno’s work has been extended, since, by Toll and by Van Kampen [5] to the case of relativistic particles with zero rest mass which formed also the subject of Kronig’s and Kramers’ early considerations [2]. Results similar to these were obtained in the course of the last years also in communication engineering, following the pioneering work of Campbell, Zobel and Foster [6], and of Cauer [7], by Brune [8], by Fränz [9] and, particularly, by Richards [10].