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

Famous quotes containing the words scattering and/or amplitude:

“A committee is organic rather than mechanical in its nature: it is not a structure but a plant. It takes root and grows, it flowers, wilts, and dies, scattering the seed from which other committees will bloom in their turn.”
—C. Northcote Parkinson (1909–1993)

“Imagination, which in truth
Is but another name for absolute power
And clearest insight, amplitude of mind,
And reason, in her most exalted mood.”
—William Wordsworth (1770–1850)