two-body relativistic scattering

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1: 29.19 Physical Applications

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§29.19(ii) Lamé Polynomials

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

2: 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.

3: 33.22 Particle Scattering and Atomic and Molecular Spectra

§33.22 Particle Scattering and Atomic and Molecular Spectra

… ►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). The motion of a relativistic electron in a Coulomb field, which arises in the theory of the electronic structure of heavy elements (Johnson (2007)), is described by a Dirac equation. … ►

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

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Solution of relativistic Coulomb equations. See for example Cooper et al. (1979) and Barnett (1981b).

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4: 15.18 Physical Applications

… ►The hypergeometric function has allowed the development of “solvable” models for one-dimensional quantum scattering through and over barriers (Eckart (1930), Bhattacharjie and Sudarshan (1962)), and generalized to include position-dependent effective masses (Dekar et al. (1999)). ►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)).

5: 28.33 Physical Applications

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Aly et al. (1975) for scattering theory.

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Jager (1997, 1998) for relativistic oscillators.

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6: 18.39 Applications in the Physical Sciences

… ►The non-relativistic Schrödinger equation describing a single, bound (negative energy) electron, in an $L^2$ eigenstate of energy $E$ is: … ►

The Relativistic Quantum Coulomb Problem

►Bound state solutions to the relativistic Dirac Equation, for this same problem of a single electron attracted by a nucleus with $Z$ protons, involve Laguerre polynomials of fractional index. … ►

The Quantum Coulomb Problem: Scattering States

… ►As the scattering eigenfunctions of Chapter 33, are not OP’s, their further discussion is deferred to §18.39(iv), where discretized representations of these scattering states are introduced, Laguerre and Pollaczek OP’s then playing a key role. …

7: Mark J. Ablowitz

… ►for appropriate data they can be linearized by the Inverse Scattering Transform (IST) and they possess solitons as special solutions. …Some of the relationships between IST and Painlevé equations are discussed in two books: Solitons and the Inverse Scattering Transform and Solitons, Nonlinear Evolution Equations and Inverse Scattering. …

8: Bibliography L

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Quantum Mechanics: Non-relativistic Theory. Pergamon Press Ltd., Oxford.

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Notes:

Revised second edition. Course of Theoretical Physics, Vol. 3. Translated from the Russian by J. B. Sykes and J. S. Bell

External Links:

MathReview, ZentralBlatt

Referenced by:

§9.16.

Encodings:

BibTeX

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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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Referenced by:

§3.10(iii), §3.10(iii), Erratum (V1.0.24) for Paragraph Steed’s Algorithm (in §3.10(iii)).

Encodings:

BibTeX

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Kinetic Theory: Classical, Quantum, and Relativistic Descriptions. third edition, Springer, New York.

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External Links:

ISBN 0387955518

Referenced by:

§18.39(iii).

Encodings:

BibTeX

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9: 14.31 Other Applications

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§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)). …

10: T. Mark Dunster

… ►He has received a number of National Science Foundation grants, and has published numerous papers in the areas of uniform asymptotic solutions of differential equations, convergent WKB methods, special functions, quantum mechanics, and scattering theory. …