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The Kramers–Heisenberg dispersion formula is an expression for the cross section for scattering of a photon by an atomic electron.It was derived before the advent of quantum mechanics by Hendrik Kramers and Werner Heisenberg in 1925, [1] based on the correspondence principle applied to the classical dispersion formula for light.
Scattering theory is the theory of scattering events which can occur as well in quantum mechanics, classical electrodynamics or acoustics. The associated general mathematical frame bears the same name though its range of application may be larger.
The following description follows the canonical way of introducing elementary scattering theory. A steady beam of particles scatters off a spherically symmetric potential V ( r ) {\displaystyle V(r)} , which is short-ranged, so that for large distances r → ∞ {\displaystyle r\to \infty } , the particles behave like free particles.
In S-matrix theory, it was stated that any quantity that one could measure should be found in the S-matrix for some process. This idea was inspired by the physical interpretation that S-matrix techniques could give to Feynman diagrams restricted to the mass-shell , and led to the construction of dual resonance models .
The Scattering transfer parameters or T-parameters of a 2-port network are expressed by the T-parameter matrix and are closely related to the corresponding S-parameter matrix. However, unlike S parameters, there is no simple physical means to measure the T parameters in a system, sometimes referred to as Youla waves.
In scattering theory, the S-matrix is an operator mapping free particle in-states to free particle out-states (scattering channels) in the Heisenberg picture. This is very useful because often we cannot describe the interaction (at least, not the most interesting ones) exactly.
The term "bootstrap model" is used for a class of theories that use very general consistency criteria to determine the form of a quantum theory from some assumptions on the spectrum of particles. It is a form of S-matrix theory.
Kramers' opacity law describes the opacity of a medium in terms of the ambient density and temperature, assuming that the opacity is dominated by bound-free absorption (the absorption of light during ionization of a bound electron) or free-free absorption (the absorption of light when scattering a free ion, also called bremsstrahlung). [1]