Tune shift with amplitude of the system. When the tune reaches resonant values, it can be unstable, and thus a tune-shift with amplitude can limit the stability region, or dynamic aperture. In classical mechanics, a simple example of a system with tune shift with amplitude is a pendulum. In accelerator physics, both the transverse and the longitudinal dynamics show tune shift with amplitude. A simple model of the transverse dynamics is of an oscillator with a single sextupole, it is referred to as the Hénon map. Another model for this case is the Standard Map. An important example is the typical case of distributed
Scattering amplitude 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 formula_2 is the position vector; formula_3; formula_4 is the incoming plane wave with the wavenumber along the axis; formula_5 is the outgoing spherical wave; is the scattering angle; and formula_6 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,