Transitions in Quantum Physical Systems—Cross Section

Abstract

This is the fundamental chapter on scattering theory. Here the concept of transition probabilities is introduced and general formulas for the cross section are derived from the basic assumptions of quantum mechanics. In Section XIV.2, a general formula for the transition rate is obtained, which will be used in Section XIV.5 for the derivation of the cross-section formula and in Chapter XXI for the derivation of the decay rate. Section XIV.3 introduces the concept of cross section, and Section XIV.4 gives a brief description of the different ways to relate the cross section to fundamental physical observables. The main section of this chapter is Section XIV.5, where the cross-section formulas for very general physical situations are derived. At the end of section XIV.5 the physical state of the scattering system is further specified to obtain the well-known expressions for the cross section. For a superficial understanding of the material of this chapter one may omit parts of Section XIV.2 and Section XIV.5. For this purpose we have discussed special results of Section XIV.5 at the end of Section XIV.4.