Scattering amplitude

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. The latter is described by the wavefunction

where ${\displaystyle \mathbf {r} \equiv (x,y,z)}$ is the position vector; ${\displaystyle r\equiv |\mathbf {r} |}$; ${\displaystyle e^{ikz}}$ is the incoming plane wave with the wavenumber ${\displaystyle k}$ along the ${\displaystyle z}$ axis; ${\displaystyle e^{ikr}/r}$ is the outgoing spherical wave; ${\displaystyle \theta }$ is the scattering angle; and ${\displaystyle f(\theta )}$ is the scattering amplitude. The dimension of the scattering amplitude is length.

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