scattering theory
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21—30 of 30 matching pages
21: 7.21 Physical Applications
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►Fried and Conte (1961) mentions the role of in the theory of linearized waves or oscillations in a hot plasma; is called the plasma dispersion
function or Faddeeva (or Faddeyeva) function; see Faddeeva and Terent’ev (1954).
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►These applications include astrophysics, plasma diagnostics, neutron diffraction, laser spectroscopy, and surface scattering.
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22: 9.16 Physical Applications
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►Details of the Airy theory are given in van de Hulst (1957) in the chapter on the optics of a raindrop.
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►Extensive use is made of Airy functions in investigations in the theory of electromagnetic diffraction and radiowave propagation (Fock (1965)).
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►Reference to many of these applications as well as to the theory of elasticity and to the heat equation are given in Vallée and Soares (2010): a book devoted specifically to the Airy and Scorer functions and their applications in physics.
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►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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23: Bibliography M
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The Theory of Groups.
Clarendon Press, Oxford.
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Crossing symmetric expansions of physical scattering amplitudes: The group and Lamé functions.
J. Mathematical Phys. 12, pp. 281–293.
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Zur Theorie des zylindrisch-parabolischen Spiegels.
Z. Physik 118, pp. 343–356 (German).
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Geometrical and Catastrophe Optics Methods in Scattering.
In Physical Acoustics, A. D. Pierce and R. N. Thurston (Eds.),
Vol. 21, pp. 1–234.
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Complex-energy method for elastic -H scattering above the ionization threshold.
Phys. Rev. Lett. 23 (7), pp. 361–363.
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24: 36.14 Other Physical Applications
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►These are the structurally stable focal singularities (envelopes) of families of rays, on which the intensities of the geometrical (ray) theory diverge.
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►Applications include scattering of elementary particles, atoms and molecules from particles and surfaces, and chemical reactions.
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25: Bibliography
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Solitons, Nonlinear Evolution Equations and Inverse Scattering.
London Mathematical Society Lecture Note Series, Vol. 149, Cambridge University Press, Cambridge.
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Solitons and the Inverse Scattering Transform.
SIAM Studies in Applied Mathematics, Vol. 4, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
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High-order interior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder.
J. Opt. Soc. Amer. A 14 (6), pp. 1305–1315.
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Scattering by singular potentials with a perturbation – Theoretical introduction to Mathieu functions.
J. Mathematical Phys. 16, pp. 961–970.
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Number Theory.
In The New Encyclopaedia Britannica,
Vol. 25, pp. 14–37.
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26: Bibliography F
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Theory and Computation of Spheroidal Harmonics with General Arguments.
Master’s Thesis, The University of Western Australia, Department of Physics.
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Semiclassical description of scattering.
Ann. Physics 7 (3), pp. 259–286.
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Application of semiclassical scattering analysis.
Ann. Physics 7 (3), pp. 287–322.
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Application of the -function theory of Painlevé equations to random matrices: PIV, PII and the GUE.
Comm. Math. Phys. 219 (2), pp. 357–398.
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Introduction to the Random Matrix Theory: Gaussian Unitary Ensemble and Beyond.
In Recent Perspectives in Random Matrix Theory and Number Theory,
London Math. Soc. Lecture Note Ser., Vol. 322, pp. 31–78.
27: Bibliography G
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Elastic scattering of photons by a hydrogen atom.
Phys. Rev. 163 (1), pp. 147–155.
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WKB and turning point theory for second-order difference equations.
In Spectral Methods for Operators of Mathematical Physics,
Oper. Theory Adv. Appl., Vol. 154, pp. 101–138.
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New method for constructing wavefunctions for bound states and scattering.
J. Chem. Phys. 51, pp. 14–25.
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Linear Differential Equations and Group Theory from Riemann to Poincaré.
2nd edition, Birkhäuser Boston Inc., Boston, MA.
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Kinetic theory of linear shear flow.
Phys. Fluids 1 (3), pp. 215–224.
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28: Bibliography V
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Light Scattering by Small Particles.
John Wiley and Sons. Inc., New York.
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Multiple Light Scattering.
Vol. 1, Academic Press, New York.
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Quantum Theory of Angular Momentum.
World Scientific Publishing Co. Inc., Singapore.
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Special Functions and the Theory of Group Representations.
American Mathematical Society, Providence, RI.
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The topological degree theory for the localization and computation of complex zeros of Bessel functions.
Numer. Funct. Anal. Optim. 18 (1-2), pp. 227–234.
29: Bibliography L
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The Classical Theory of Fields.
Pergamon Press, Oxford.
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Essai sur la Théorie des Nombres.
2nd edition, Courcier, Paris.
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Generating Bessel functions in Mie scattering calculations using continued fractions.
Applied Optics 15 (3), pp. 668–671.
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Zur Theorie der Gaußschen Summen.
Math. Ann. 57 (4), pp. 554–567 (German).
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Kinetic Theory: Classical, Quantum, and Relativistic Descriptions.
third edition, Springer, New York.
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30: Bibliography Y
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-matrix method: Extensions to arbitrary angular momentum and to Coulomb scattering.
J. Math. Phys. 16, pp. 410–420.
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Mathematical Apparatus of the Theory of Angular Momentum.
Israel Program for Scientific Translations for National Science
Foundation and the National Aeronautics and Space Administration, Jerusalem.