A discrete version of the inverse scattering problem

Abstract

A discrete version of the inverse scattering problem is considered. The Schrödinger equation with a potential is replaced by a difference equation. The problem is to determine the coefficients given the phase shift. Application is mainly pedagogical. The motivation for the principal steps becomes obvious and the mathematics is elementary. At any stage one can pass, by a limiting procedure, to the usual Schrödinger problem-and reobtain the classical results.