The coherent potential approximation (or CPA) is a method, in

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which rel ...

, of finding the

Green's function In mathematics, a Green's function is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions. This means that if \operatorname is the linear differenti ...

of an effective medium. It is a useful concept in understanding how

sound waves In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by th ...

scatter in a material which displays spatial inhomogeneity. One version of the CPA is an extension to random materials of the

muffin-tin approximation The muffin-tin approximation is a shape approximation of the potential well in a crystal lattice. It is most commonly employed in quantum mechanical simulations of the electronic band structure in solids. The approximation was proposed by Joh ...

, used to calculate

electronic band structure In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called ''band gaps'' or ...

in solids. A variational implementation of the muffin-tin approximation to crystalline solids using

s was suggested by Korringa and by Kohn and Rostoker, and is often referred to as the KKR method. For random materials, the theory is applied by the introduction of an ordered lattice of effective potentials to replace the varying potentials in the random material. This approach is called the ''KKR coherent potential approximation''.

References

Further reading