In quantum physics, the scattering amplitude is the probability amplitude of the outgoing spherical wave relative to the incoming plane wave in a stationary-state scattering process. The plane wave is described by the wavefunction where is the position vector; ; is the incoming plane wave with the wavenumber along the axis; is the outgoing spherical wave; is the scattering angle; and is the scattering amplitude. The dimension of the scattering amplitude is length. The scattering amplitude is a probability amplitude; the differential cross-section as a function of scattering angle is given as its modulus squared, X-rays The scattering length for X-rays is the Thomson scattering length or classical electron radius, 0. Neutrons The nuclear neutron scattering process involves the coherent neutron scattering length, often described by . Quantum mechanical formalism A quantum mechanical approach is given by the S matrix formalism. Measurement The scattering amplitude can be determined by the scattering length in the low-energy regime. See also Veneziano amplitude Plane wave expansion References Neutron X-rays Electron Scattering Diffraction