Scattering Amplitude

In quantum physics, the scattering amplitude is the amplitude of the outgoing spherical wave relative to the incoming plane wave in the stationary-state scattering process. The latter is described by the wavefunction

\psi(\mathbf{r}) = e^{ikz} + f(\theta)\frac{e^{ikr}}{r} \;,

where is the coordinate vector; ; is the incoming plane wave with the wave-vector 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 differential cross-section is given as

\frac{d\sigma}{d\Omega} = |f(\theta)|^2 \;.

In the low-energy regime the scattering amplitude is determined by the scattering length.

Read more about Scattering Amplitude:  Partial Wave Expansion, X-rays, Neutrons, Quantum Mechanical Formalism

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