Scattering amplitude

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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] The plane wave is described by the wavefunction

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; 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 scattering length for X-rays is the Thomson scattering length or classical electron radius, r0.


The nuclear neutron scattering process involves the coherent neutron scattering length, often described by b.

Quantum mechanical formalism[edit]

A quantum mechanical approach is given by the S matrix formalism.


The scattering amplitude can be determined by the scattering length in the low-energy regime.

See also[edit]


  1. ^ Quantum Mechanics: Concepts and Applications Archived 2010-11-10 at the Wayback Machine By Nouredine Zettili, 2nd edition, page 623. ISBN 978-0-470-02679-3 Paperback 688 pages January 2009