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:

    “Or of the garden where we first mislaid
    Simplicity of wish and will, forgetting
    Out of what cognate splendor all things came
    To take their scattering names;”
    —Richard Wilbur (b. 1921)

    “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)