Scattering theory

Summary

Scattering theory studies how a quantum system that is free in the far past interacts and becomes free again in the far future. It compares the dynamics generated by a full Hamiltonian $H$ with the dynamics of a simpler free Hamiltonian $H_0$ for large positive and negative times. Its main objects are the wave operators and the S-matrix, which map incoming free states to outgoing free states. It is the mathematical basis of collision experiments in atomic, nuclear and particle physics, and has close analogues for classical waves.