J-Matrix Theory of Scattering

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11: 36.14 Other Physical Applications

… ►These are the structurally stable focal singularities (envelopes) of families of rays, on which the intensities of the geometrical (ray) theory diverge. … ►Applications include scattering of elementary particles, atoms and molecules from particles and surfaces, and chemical reactions. …

12: 10.73 Physical Applications

… ►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. … … ►In the theory of plates and shells, the oscillations of a circular plate are determined by the differential equation … ►

§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. …

13: 5.20 Physical Applications

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Rutherford Scattering

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Elementary Particles

►Veneziano (1968) identifies relationships between particle scattering amplitudes described by the beta function, an important early development in string theory. …

14: Bibliography Y

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$J$-matrix method: Extensions to arbitrary angular momentum and to Coulomb scattering. J. Math. Phys. 16, pp. 410–420.

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Referenced by:

§18.39(iv).

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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.

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Notes:

Translated from the Russian by A. Sen and R. N. Sen

External Links:

MathReview (R. F. Stora), ZentralBlatt

Referenced by:

§34.11.

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15: 26.19 Mathematical Applications

§26.19 Mathematical Applications

… ►Partitions and plane partitions have applications to representation theory (Bressoud (1999), Macdonald (1995), and Sagan (2001)) and to special functions (Andrews et al. (1999) and Gasper and Rahman (2004)). ►Other areas of combinatorial analysis include graph theory, coding theory, and combinatorial designs. These have applications in operations research, probability theory, and statistics. …

16: 33.22 Particle Scattering and Atomic and Molecular Spectra

§33.22 Particle Scattering and Atomic and Molecular Spectra

… ►Positive-energy functions correspond to processes such as Rutherford scattering and Coulomb excitation of nuclei (Alder et al. (1956)), and atomic photo-ionization and electron-ion collisions (Bethe and Salpeter (1977)). … ►

§33.22(iv) Klein–Gordon and Dirac Equations

►The relativistic motion of spinless particles in a Coulomb field, as encountered in pionic atoms and pion-nucleon scattering (Backenstoss (1970)) is described by a Klein–Gordon equation equivalent to (33.2.1); see Barnett (1981a). … ►

Scattering at complex energies. See for example McDonald and Nuttall (1969).

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17: Bibliography R

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Plane wave scattering by a conducting elliptic cylinder coated by a nonconfocal dielectric. IEEE Trans. Antennas and Propagation 39 (2), pp. 218–223.

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External Links:

Document

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6th item.

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Methods of Modern Mathematical Physics, Vol. 3, Scattering Theory. Academic Press, New York.

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External Links:

ISBN 0-12-585003-4 (vol.3), MathReview (P. R. Chernoff)

Referenced by:

§1.18(x).

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Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse. Inauguraldissertation, Göttingen.

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Referenced by:

§21.7(i).

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Elementary Number Theory and its Applications. 5th edition, Addison-Wesley, Reading, MA.

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External Links:

ISBN 0-201-87073-8, MathReview (Norman J. Richert)

Referenced by:

§27.17.

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On the foundations of combinatorial theory. I. Theory of Möbius functions. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 2, pp. 340–368.

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External Links:

Document, MathReview (M. A. Harrison), ZentralBlatt

Referenced by:

§27.5.

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18: 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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External Links:

ISBN 0-521-38730-2, Document, Link, MathReview (Walter Oevel), ZentralBlatt

Referenced by:

§22.19(ii), §22.19(iii), §32.11(ii), §32.5, §9.16, Profile Mark J. Ablowitz, Profile Peter A. Clarkson.

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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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External Links:

ISBN 0-89871-174-6, MathReview (Benno Fuchssteiner), ZentralBlatt

Referenced by:

§21.9, §21.9, §32.5, §9.16, Profile Mark J. Ablowitz.

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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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FullText

Referenced by:

§36.14(ii).

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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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Notes:

Erratum: same journal 17 (1975), no. 7, p. 1361

External Links:

Document, MathReview (K. Veselic), ZentralBlatt

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4th item.

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Number Theory. In The New Encyclopaedia Britannica, Vol. 25, pp. 14–37.

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Referenced by:

§27.13(i), §27.15, §27.16, Ch.27.

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19: 7.21 Physical Applications

… ►Fried and Conte (1961) mentions the role of $w\left(z\right)$ in the theory of linearized waves or oscillations in a hot plasma; $w\left(z\right)$ is called the plasma dispersion function or Faddeeva (or Faddeyeva) function; see Faddeeva and Terent’ev (1954). … ►These applications include astrophysics, plasma diagnostics, neutron diffraction, laser spectroscopy, and surface scattering. …

20: 28.33 Physical Applications

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Aly et al. (1975) for scattering theory.

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Fukui and Horiguchi (1992) for quantum theory.

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