scattering theory

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11: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►this being a matrix element of the resolvent $F(T)={\left(z-T\right)}^{-1}$, this being a key quantity in many parts of physics and applied math, quantum scattering theory being a simple example, see Newton (2002, Ch. 7). … ►which appear in the quantum theory of binding or scattering of a particle in a spherically symmetric potential $V(r)$ in three dimensions, and where $r\in [0,\mathrm{\infty })$. …

12: 15.18 Physical Applications

… ►More varied applications include photon scattering from atoms (Gavrila (1967)), energy distributions of particles in plasmas (Mace and Hellberg (1995)), conformal field theory of critical phenomena (Burkhardt and Xue (1991)), quantum chromo-dynamics (Atkinson and Johnson (1988)), and general parametrization of the effective potentials of interaction between atoms in diatomic molecules (Herrick and O’Connor (1998)).

13: 5.20 Physical Applications

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

14: 27.17 Other Applications

… ►Schroeder (2006) describes many of these applications, including the design of concert hall ceilings to scatter sound into broad lateral patterns for improved acoustic quality, precise measurements of delays of radar echoes from Venus and Mercury to confirm one of the relativistic effects predicted by Einstein’s theory of general relativity, and the use of primes in creating artistic graphical designs.

15: 29.19 Physical Applications

… ►Bronski et al. (2001) uses Lamé functions in the theory of Bose–Einstein condensates. ►

§29.19(ii) Lamé Polynomials

… ►Macfadyen and Winternitz (1971) finds expansions for the two-body relativistic scattering amplitudes. …

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: 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. …

18: Bibliography K

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Replica field theories, Painlevé transcendents, and exact correlation functions. Phys. Rev. Lett. 89 (25), pp. (250201–1)–(250201–4).

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External Links:

ISSN 0031-9007, Document, MathReview, ZentralBlatt

Referenced by:

§32.16.

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The Scattering of Light and Other Electromagnetic Radiation. Academic Press, New York.

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External Links:

ISBN 0-12-404550-2

Referenced by:

§10.73(i).

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Neue Untersuchungen einer Reihe aus der Theorie der elliptischen Funktionen. Journal für die Reine und Angenwandte Mathematik 158, pp. 209–218 (German).

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External Links:

ZentralBlatt

Referenced by:

§19.5.

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Zur Theorie der Modulformen $n$-ten Grades. I. Math. Z. 59, pp. 399–416 (German).

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ISSN 0025-5874, Document, MathReview (H. S. Zuckerman), ZentralBlatt

Referenced by:

§35.6(i).

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Quantum Inverse Scattering Method and Correlation Functions. Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-37320-4; 0-521-58646-1, MathReview (Makoto Idzumi), ZentralBlatt

Referenced by:

§26.20.

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19: 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 $P_{\nu }\left(x\right)$ of complex degree $\nu$ appear in the application of complex angular momentum techniques to atomic and molecular scattering (Connor and Mackay (1979)). …

20: Bibliography S

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The Laplace Transform: Theory and Applications. Undergraduate Texts in Mathematics, Springer-Verlag, New York.

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External Links:

ISBN 0-387-98698-7, MathReview (Philip Heywood), ZentralBlatt

Referenced by:

§1.14(iii), §1.14(vii).

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Use of analyticity in the calculation of nonrelativistic scattering amplitudes. Phys. Rev. 167, pp. 1411–1423.

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External Links:

Document, Link

Referenced by:

(18.40.9), §18.40(ii).

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Variational calculations of scattering. Ann. Phys. 16, pp. 36–50.

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Referenced by:

§18.39(iv).

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Quantum defect theory. Rep. Prog. Phys. 46 (2), pp. 167–257.

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External Links:

Document

Referenced by:

§33.14(i), §33.22(ii).

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Practical Extrapolation Methods: Theory and Applications. Cambridge Monographs on Applied and Computational Mathematics, Vol. 10, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-66159-5, MathReview (Thomas A. Atchison), ZentralBlatt

Referenced by:

§3.9(vi).

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