Mathematical Foundation of the Scattering Problem

Abstract

This chapter is devoted to justification of the hypothesis about completeness of the wave operators. We will present the reasoning for the system consisting of two and three particles. First, we describe the methods used for the investigation of the continuous spectrum of the energy operator in the stationary formalism. In this part, the results of this chapter overlap with those of Chapter 2, where we have been working in the framework of the non-stationary approach. Together with these issues, we will proceed here with the study of the Coulomb problem: we will calculate the kernels of the scattering operator for charged particles and describe their properties. At the end of this chapter we will verify that the kernels of the wave operators, obtained by using the stationary formalism, coincide with kernels of the non-stationary wave operators (1.22) and (1.25) depending on the character of the pair interactions.