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1: 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)). …

2: 5.20 Physical Applications

§5.20 Physical Applications

… ►In nonrelativistic quantum mechanics, collisions between two charged particles are described with the aid of the Coulomb phase shift $\mathrm{ph}\mathrm{\Gamma }\left(\mathrm{\ell }+1+\mathrm{i}\eta \right)$; see (33.2.10) and Clark (1979). … ►

Elementary Particles

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

3: 36.14 Other Physical Applications

§36.14 Other Physical Applications

… ►The physical manifestations of bifurcation sets are caustics. … ►Applications include scattering of elementary particles, atoms and molecules from particles and surfaces, and chemical reactions. …

4: Bibliography M

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A dispersion function for plasmas containing superthermal particles. Physics of Plasmas 2 (6), pp. 2098–2109.

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External Links:

Document

Referenced by:

§15.18.

Encodings:

BibTeX

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Spherical Harmonics. An Elementary Treatise on Harmonic Functions with Applications. 3rd edition, International Series of Monographs in Pure and Applied Mathematics, Vol. 98, Pergamon Press, Oxford.

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External Links:

MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

Ch.14.

Encodings:

BibTeX

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On the interval computation of elementary functions. C. R. Acad. Bulgare Sci. 34 (3), pp. 319–322.

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External Links:

ISSN 0366-8681, MathReview (David F. Griffiths), ZentralBlatt

Referenced by:

§4.45(i).

Encodings:

BibTeX

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CODATA recommended values of the fundamental physical constants: 2002. Rev. Mod.Phys. 77, pp. 1–107.

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Referenced by:

§18.39(ii).

Encodings:

BibTeX

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Elementary Functions: Algorithms and Implementation. Birkhäuser Boston Inc., Boston, MA.

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Notes:

A 2nd edition was published in 2006.

External Links:

ISBN 0-8176-3990-X, MathReview (Warren E. Ferguson, Jr.), ZentralBlatt

Referenced by:

§4.45(i).

Encodings:

BibTeX

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5: 33.22 Particle Scattering and Atomic and Molecular Spectra

§33.22 Particle Scattering and Atomic and Molecular Spectra

… ►With $\mathrm{e}$ denoting here the elementary charge, the Coulomb potential between two point particles with charges $Z_1\mathrm{e},Z_2\mathrm{e}$ and masses $m_1,m_2$ separated by a distance $s$ is $V(s)=Z_1{Z}_2{\mathrm{e}}^2/(4\pi {\epsilon }_{0}s)=Z_1{Z}_2\alpha \mathrm{\hslash }c/s$, where $Z_j$ are atomic numbers, ${\epsilon }_0$ is the electric constant, $\alpha$ is the fine structure constant, and $\mathrm{\hslash }$ is the reduced Planck’s constant. … ►Customary variables are $(ϵ,r)$ in atomic physics and $(\eta ,\rho )$ in atomic and nuclear physics. … ►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). … ►For scattering problems, the interior solution is then matched to a linear combination of a pair of Coulomb functions, $F_{\mathrm{\ell }}(\eta ,\rho )$ and $G_{\mathrm{\ell }}(\eta ,\rho )$, or $f(ϵ,\mathrm{\ell };r)$ and $h(ϵ,\mathrm{\ell };r)$, to determine the scattering $S$-matrix and also the correct normalization of the interior wave solutions; see Bloch et al. (1951). …