Scattering amplitude

A complex quantity that encodes the probability and phase of a quantum transition or scattering outcome; its squared magnitude gives the corresponding probability or differential cross section.

Born rule: The quantum rule that assigns probabilities from squared amplitudes. It turns a transition amplitude’s magnitude into an outcome probability.
Quantum state: A mathematical description of a quantum system’s physical state. Amplitudes connect particular initial and final quantum states.
Møller scattering: The scattering of two electrons through their electromagnetic interaction. Its amplitudes give predictions for electron–electron collision rates.
Probability amplitude: A complex quantum quantity whose squared magnitude gives the probability of an outcome. It is the broader quantum concept of which scattering amplitudes are a specialized instance.
S-matrix: The operator that maps incoming quantum states to outgoing states in a scattering process. Its matrix elements are scattering amplitudes between specified states.
Transition matrix element: A matrix element of an operator between specified initial and final states. Scattering amplitudes are transition matrix elements, often of the S-matrix.
Bhabha scattering: The scattering of an electron and a positron into an electron and a positron. Its calculated amplitude is a standard test of quantum electrodynamics.
Scattering cross section: A measure of the effective area governing the likelihood of a scattering event. Unlike an amplitude, a cross section is an observable probability measure.
Differential cross section: A measure of scattering probability per incident flux and per unit solid angle or other final-state interval. Its angular distribution is proportional to the squared scattering amplitude.
Complex number: A number with real and imaginary parts, expressible by magnitude and phase. Amplitude phases affect interference even when probabilities use squared magnitudes.

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