particle scattering
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11: 14.31 Other Applications
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§14.31(ii) Conical Functions
… ►These functions are also used in the Mehler–Fock integral transform (§14.20(vi)) for problems in potential and heat theory, and in elementary particle physics (Sneddon (1972, Chapter 7) and Braaksma and Meulenbeld (1967)). … ►§14.31(iii) Miscellaneous
►Many additional physical applications of Legendre polynomials and associated Legendre functions include solution of the Helmholtz equation, as well as the Laplace equation, in spherical coordinates (Temme (1996b)), quantum mechanics (Edmonds (1974)), and high-frequency scattering by a sphere (Nussenzveig (1965)). … ►Legendre functions of complex degree appear in the application of complex angular momentum techniques to atomic and molecular scattering (Connor and Mackay (1979)). …12: 10.73 Physical Applications
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►Bessel functions enter in the study of the scattering of light and other electromagnetic radiation, not only from cylindrical surfaces but also in the statistical analysis involved in scattering from rough surfaces.
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§10.73(ii) Spherical Bessel Functions
… ►Accordingly, the spherical Bessel functions appear in all problems in three dimensions with spherical symmetry involving the scattering of electromagnetic radiation. …In quantum mechanics the spherical Bessel functions arise in the solution of the Schrödinger wave equation for a particle in a central potential. …13: 9.16 Physical Applications
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►An example from quantum mechanics is given in Landau and Lifshitz (1965), in which the exact solution of the Schrödinger equation for the motion of a particle in a homogeneous external field is expressed in terms of .
…A study of the semiclassical description of quantum-mechanical scattering is given in Ford and Wheeler (1959a, b).
In the case of the rainbow, the scattering amplitude is expressed in terms of , the analysis being similar to that given originally by Airy (1838) for the corresponding problem in optics.
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