ABSTRACT
This chapter discusses a particular kind of state, called a resonance, which has its origin in the analytic structure of the scattering amplitude. The basis of the quantum theory of scattering is the time-dependent Schrodinger equation. The most obvious choice is the partial wave decomposition of the scattering amplitude in which case the index n corresponds to the total angular momentum of the system. A rapid change in the phase of one partial scattering amplitude may be due to the presence of a pole in the complex k-plane. In general, each partial scattering amplitude has many poles, and their effect on the scattered wave packet depends on how they are grouped together. The theory has been developed by Bohr-Sommerfeld and Watson-Sommerfeld for electromagnetic scattering processes, and later it was extended by Regge poles and Alfaro and Regge to quantum scattering processes, particularly for the case of nuclear and elementary particle scattering.
