ABSTRACT
This chapter presents a modernized version of a method originally due to Dirac. This approach depends on a straightforward expansion in powers of the perturbing interaction. The chapter examines a problem where the unperturbed Hamiltonian had a discrete spectrum, and the perturbation was explicitly time dependent. The situation where the spectrum is continuous and the perturbation is independent of time is encountered much more frequently in physics. The chapter explores the derivations of some rather general formulas for collision cross sections. The photo-effect in hydrogen constitutes a very interesting example of a perturbation problem. The dramatic behavior of the matrix element demonstrates that at low energy the Coulomb attraction is very effective in keeping the slow photo-electron near the origin. The chapter examines the result of a collision experiment. It aims to illustrate the power and limitations of the technique, and to establish its relationship to the treatment of elastic scattering.
