Scattering in Classical and Quantum Physics

Abstract

Scattering experiments provide the main source of information on the properties of elementary particles. Here we present the theory of scattering in both classical and non-relativistic quantum physics. We introduce the basic notions of cross section and of range and strength of interactions. We work out some illustrative examples. The concept of resonant scattering, central to almost all applications in particle physics, is explained in the simple case of potential scattering, where we derive the Breit–Wigner formula. This framework of non-relativistic potential scattering turns out to be very convenient for introducing several other important concepts and results, such as the optical theorem, the partial wave amplitudes and the corresponding phase shifts and scattering lengths. The special cases of scattering at low energies, and that in the Born approximation, are studied. We also offer a first glance at the problem of the infrared divergences for the case of Coulomb scattering.