The Inverse Problem in the Quantum Theory of Scattering

TLDR

This report translates a 1959 Russian survey by L. D. Faddeyev on scattering theory, noting that similar inverse scattering questions arise in quantum mechanics. The authors aim to reproduce and distribute the translation because it addresses the inverse scattering problem of inferring medium properties from reflection coefficients. They provide a translation of Faddeyev’s 1959 survey, making it available to a wider audience.

Abstract

This report is a translation from the Russian of a survey article by L. D. Faddeyev, which appeared in Uspekhi Matem. Nauk., 14, 57 (1959). Our own interest in this article lies in its relevance to the inverse scattering problem—that is, the problem of determining information about a medium from which an electromagnetic wave is reflected, given a knowledge of the reflection coefficient. Similar questions concerning scattering phenomena in other branches of physics, e.g., in quantum mechanics, can be investigated by means of the same theory. We have therefore thought it worth-while to reproduce and distribute the translation. A good indication of the contents is given in the Introduction.