One Dimensional Scattering Problems: A Pedagogical Presentation of the Relationship between Reflection and Transmission Amplitudes

Petarpa Boonserm, Matt Visser

Abstract

In this article we provide a pedagogical introduction to scattering theory in one space dimension. This is an elegant topic that is mathematically simple and physically transparent. We shall apply the Schrodinger equation to a generic system to identify the Bogoliubov coefficients. Furthermore, we shall then derive a number of significant relationships between reflection and transmission amplitudes.