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Multiple scattering theory (MST) is the mathematical formalism that is used to describe the propagation of a wave through a collection of scatterers. Examples are acoustical waves traveling through porous media, light scattering from water droplets in a cloud, or x-rays scattering from a crystal. A more recent application is to the propagation of quantum matter waves like electrons or neutrons through a solid.
As pointed out by Jan Korringa, the origin of this theory can be traced back to an 1892 paper by Lord Rayleigh. An important mathematical formulation of the theory was made by Paul Peter Ewald. Korringa and Ewald acknowledged the influence on their work of the 1903 doctoral dissertation of Nikolai Kasterin, portions of which were published in German in the Proceedings of the Royal Academy of Sciences in Amsterdam under the sponsorship of Heike Kamerlingh Onnes. The MST formalism is widely used for electronic structure calculations as well as diffraction theory, and is the subject of many books.The multiple-scattering approach is the best way to derive one-electron Green's functions. These functions differ from the Green's functions used to treat the many-body problem, but they are the best starting point for calculations of the electronic structure of condensed matter systems that cannot be treated with band theory.
The terms "multiple scattering" and "multiple scattering theory" are often used in other contexts. For example, Molière's theory of the scattering of fast charged particles in matter is described in that way.