text: 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. 
  At large distances from the centrally symmetric scattering center, 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 (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
  where  is the direction of incidient particles and  is the direction of scattered particles.