Scattering theory studies incoming states, outgoing states, and the probability that an interaction deflects a particle or wave. The measurable result is often encoded in a cross section, which quantifies the effective size of the target for a given process.

The differential cross section $d\sigma/d\Omega$ gives the angular distribution of scattered particles. It is central in particle physics, nuclear physics, and atomic collisions. For weak scattering, the Born approximation provides a first estimate using the Fourier transform of the potential.

For central potentials, the scattering amplitude can be decomposed into partial waves labeled by angular momentum quantum number $l$. The effect of the potential appears as a phase shift $\delta_l$, which determines how each partial wave is modified relative to free motion.