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In mathematical physics, scattering theory is a framework for studying and understanding the interaction or scattering of solutions to partial differential equations. In acoustics , the differential equation is the wave equation , and scattering studies how its solutions, the sound waves , scatter from solid objects or propagate through non ...
Mie scattering (sometimes referred to as a non-molecular scattering or aerosol particle scattering) takes place in the lower 4,500 m (15,000 ft) of the atmosphere, where many essentially spherical particles with diameters approximately equal to the wavelength of the incident ray may be present. Mie scattering theory has no upper size limitation ...
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.
Scattering from any spherical particles with arbitrary size parameter is explained by the Mie theory. Mie theory, also called Lorenz-Mie theory or Lorenz-Mie-Debye theory, is a complete analytical solution of Maxwell's equations for the scattering of electromagnetic radiation by spherical particles (Bohren and Huffman, 1998).
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.
X = total number of particles falling on the scattering material; n = number of atoms in a unit volume of the material; t = thickness of the foil; q n = positive charge of the atomic nucleus; q a = positive charge of the alpha particles; m = mass of an alpha particle; v = velocity of the alpha particle; Rutherford scattering cross-section is ...
The equation was later extended to quantum scattering theory by several individuals, and came to be known as the Bohr–Peierls–Placzek relation after a 1939 paper. It was first referred to as the "optical theorem" in print in 1955 by Hans Bethe and Frederic de Hoffmann , after it had been known as a "well known theorem of optics" for some time.