Introduction

Historically, data regarding quantum phenomena was obtained from two main sources. Firstly, the study of spectroscopic lines, and, secondly, the analysis of data from scattering experiments. We have already developed theories that account for some aspects of the spectra of hydrogen-like atoms. Let us now examine the quantum theory of scattering.

In the following, we shall treat scattering as an essentially two-particle effect. As is well known, when viewed in the center of mass frame, two particles of masses $m_1$ and $m_2$ , and position vector ${\bf x}_1$ and ${\bf x}_2$ , respectively, interacting via the potential $V({\bf x}_1-{\bf x}_2)$ , can be treated as a single body of reduced mass $\mu_{12}=m_1\,m_2/(m_1+m_2)$ , and position vector ${\bf x}={\bf x}_1-{\bf x}_2$ , moving in the fixed potential $V({\bf x})$ [50]. For this reason, we can, without loss of generality, focus our study on the quantum theory of particles scattered by fixed potentials.