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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 ...
In mathematics and physics, the inverse scattering problem is the problem of determining characteristics of an object, based on data of how it scatters incoming radiation or particles. [1] It is the inverse problem to the direct scattering problem, which is to determine how radiation or particles are scattered based on the properties of the ...
An animation of the figure-8 solution to the three-body problem over a single period T ≃ 6.3259 [13] 20 examples of periodic solutions to the three-body problem. In the 1970s, Michel Hénon and Roger A. Broucke each found a set of solutions that form part of the same family of solutions: the Broucke–Hénon–Hadjidemetriou family. In this ...
In physical problems, this differential equation must be solved with the input of an additional set of initial and/or boundary conditions for the specific physical system studied. The Lippmann–Schwinger equation is equivalent to the Schrödinger equation plus the typical boundary conditions for scattering problems.
In the standard scattering problem, the incoming beam is assumed to take the form of a plane wave of wave number k, which can be decomposed into partial waves using the plane-wave expansion in terms of spherical Bessel functions and Legendre polynomials:
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.
Solutions to the equation of radiative transfer form an enormous body of work. The differences however, are essentially due to the various forms for the emission and absorption coefficients. If scattering is ignored, then a general steady state solution in terms of the emission and absorption coefficients may be written:
For three-dimensional problems, one would calculate the scattering cross-section, which, roughly speaking, is the total area of the incident beam which is scattered. Another quantity of relevance is the partial cross-section , σ l {\displaystyle \sigma _{\text{l}}} , which denotes the scattering cross section for a partial wave of a definite ...