relativistic Coulomb equations

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1: 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. … ►

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

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2: 18.39 Applications in the Physical Sciences

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§18.39(ii) A 3D Separable Quantum System, the Hydrogen Atom

… ►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. … ►

Discretized and Continuum Expansions of Scattering Eigenfunctions in terms of Pollaczek Polynomials: J-matrix Theory

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3: 13.28 Physical Applications

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§13.28(i) Exact Solutions of the Wave Equation

►The reduced wave equation ${\nabla }^{2}w=k^{2}w$ in paraboloidal coordinates, $x=2\sqrt{\xi \eta }\cos \varphi$, $y=2\sqrt{\xi \eta }\sin \varphi$, $z=\xi -\eta$, can be solved via separation of variables $w=f_1(\xi )f_2(\eta ){\mathrm{e}}^{\mathrm{i}p\varphi }$, where …and $V_{\kappa ,\mu }^{(j)}(z)$, $j=1,2$, denotes any pair of solutions of Whittaker’s equation (13.14.1). … ►

§13.28(ii) Coulomb Functions

… ►For dynamics of many-body systems see Meden and Schönhammer (1992); for tomography see D’Ariano et al. (1994); for generalized coherent states see Barut and Girardello (1971); for relativistic cosmology see Crisóstomo et al. (2004).

4: Bibliography P

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Sur les équations différentielles du second ordre à points critiques fixès. C.R. Acad. Sc. Paris 143, pp. 1111–1117.

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External Links:

ZentralBlatt

Referenced by:

§32.2(iv).

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Smoothing of the Stokes phenomenon for high-order differential equations. Proc. Roy. Soc. London Ser. A 436, pp. 165–186.

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External Links:

ISSN 0962-8444, FullText, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§2.11(v).

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A uniform asymptotic expansion for the incomplete gamma function. J. Comput. Appl. Math. 148 (2), pp. 323–339.

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ISSN 0377-0427, Document, MathReview (Dumitru Acu), ZentralBlatt

Referenced by:

(8.11.6), §8.11(iii), (8.12.18), §8.12, §8.12, §8.12, Erratum (V1.0.16) for Equation (8.12.18).

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Recurrence formulas for Coulomb wave functions. Physical Rev. (2) 72 (7), pp. 626–627.

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Document, MathReview (S. C. van Veen), ZentralBlatt

Referenced by:

§33.4.

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Comoving coordinate system for relativistic hydrodynamics. Phy. Rev. C 75, pp. (024907–1)–(024907–10).

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Document

Referenced by:

§7.21.

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5: Bibliography G

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Algorithm 292: Regular Coulomb wave functions. Comm. ACM 9 (11), pp. 793–795.

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ISSN 0001-0782, Document

Referenced by:

§33.26(ii).

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The Computation of Special Functions by Linear Difference Equations. In Advances in Difference Equations (Veszprém, 1995), S. Elaydi, I. Győri, and G. Ladas (Eds.), pp. 213–243.

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ISBN 90-5699-521-9, MathReview, ZentralBlatt

Referenced by:

§3.6(iii), §3.6(vii).

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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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ISBN 0-8176-3837-7, MathReview, ZentralBlatt

Referenced by:

§15.17(v).

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Quantum Electrodynamics of Strong Fields: With an Introduction into Modern Relativistic Quantum Mechanics. Texts and Monographs in Physics, Springer.

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Referenced by:

§33.22(iv).

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Algorithm 300: Coulomb wave functions. Comm. ACM 10 (4), pp. 244–245.

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Notes:

For remarks see same journal 12(1969), p. 692 and 16(1973), pp. 308-309 and for certification see same journal 12(1969), pp. 279-280.

External Links:

ISSN 0001-0782, Document

Referenced by:

§33.26(ii).

Encodings:

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