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The Korringa–Kohn–Rostoker (KKR) method is used to calculate the electronic band structure of periodic solids.In the derivation of the method using multiple scattering theory by Jan Korringa [1] and the derivation based on the Kohn and Rostoker variational method, [2] the muffin-tin approximation was used. [3]
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.
It relates the scattered wave function with the interaction that produces the scattering (the scattering potential) and therefore allows calculation of the relevant experimental parameters (scattering amplitude and cross sections). The most fundamental equation to describe any quantum phenomenon, including scattering, is the Schrödinger equation.
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.
In scattering theory, a scattering channel is a quantum state of the colliding system before or after the collision (). The Hilbert space spanned by the states before collision (in states) is equal to the space spanned by the states after collision (out states) which are both Fock spaces if there is a mass gap .
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.
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.
In quantum field theory, the Lehmann–Symanzik–Zimmermann (LSZ) reduction formula is a method to calculate S-matrix elements (the scattering amplitudes) from the time-ordered correlation functions of a quantum field theory.