Scattering amplitude
Probability amplitude in quantum scattering theory / From Wikipedia, the free encyclopedia
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.[1] At large distances from the centrally symmetric scattering center, the plane wave is described by the wavefunction[2]
where is the position vector;
;
is the incoming plane wave with the wavenumber k along the z axis;
is the outgoing spherical wave; θ is the scattering angle (angle between the incident and scattered direction); 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,
The asymptotic form of the wave function in arbitrary external field takes the form[2]
where is the direction of incidient particles and
is the direction of scattered particles.