 Quantum scattering

Quantum scattering relates incoming and outgoing states of an interaction problem. For a short-range potential in three dimensions, a stationary asymptotic solution is often written $\psi \sim e^{ikz}+f(\theta ,\phi )e^{ikr}/r$: the incident plane wave and outgoing spherical wave define the scattering amplitude $f$.

For equal incoming/outgoing speeds and the stated normalization, $d\sigma /d\Omega =|f{|}^2$ connects that amplitude to detector counts. Phases matter because alternative contributions interfere before their probabilities are formed. A normalizable wave packet supplies a physical incident preparation, while ideal stationary states simplify the asymptotic calculation. Long-range Coulomb interactions require modified asymptotic treatment, and internal excitations create additional channels. Partial-wave scattering uses angular momentum to organize a central-potential problem into simpler radial channels.