angular momentum

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1: Brian R. Judd

… ► Elliott), published by Caxton Press in 1971, and Angular Momentum Theory for Diatomic Molecules, published by Academic Press in 1975. …

2: Bibliography Y

… ►

H. A. Yamani and L. Fishman (1975)

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).
Encodings:: BibTeX

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A. P. Yutsis, I. B. Levinson, and V. V. Vanagas (1962) 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.
Encodings:: BibTeX

3: 16.24 Physical Applications

… ►

§16.24(iii) $\mathit{3j}$ , $\mathit{6j}$ , and $\mathit{9j}$ Symbols

…

4: 34.1 Special Notation

… ►

34.1.1

\left(j_{1}\;m_{1}\;j_{2}\;m_{2}|j_{1}\;j_{2}\;j_{3}\,\,m_{3}\right)=(-1)^{j_{% 1}-j_{2}+m_{3}}(2j_{3}+1)^{\frac{1}{2}}\begin{pmatrix}j_{1}&j_{2}&j_{3}\\ m_{1}&m_{2}&-m_{3}\end{pmatrix};

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Symbols:: $\begin{pmatrix}\NVar{j_{1}}&\NVar{j_{2}}&\NVar{j_{3}}\\ \NVar{m_{1}}&\NVar{m_{2}}&\NVar{m_{3}}\end{pmatrix}$ : $\mathit{3j}$ symbol and $j,j_{r}$ : non-negative integers or non-negative integers plus one half.
Sources:: Edmonds (1974, p. 46, Eq. (3.7.3)); Rotenberg et al. (1959, p. 1, Eq. (1.1a))
Permalink:: http://dlmf.nist.gov/34.1.E1
Encodings:: pMML, png, TeX
Clarification (effective with 1.0.15):: A wording change reflects that the Clebsch–Gordan coefficients are an alternative formulation of angularmomentum problems, rather than alternative notation for the $\mathit{3j}$ . The sign of $m_{3}$ was changed for clarity.
See also:: Annotations for §34.1 and Ch.34

… ►For other notations for

\mathit{3j}

\mathit{6j}

\mathit{9j}

symbols, see Edmonds (1974, pp. 52, 97, 104–105) and Varshalovich et al. (1988, §§8.11, 9.10, 10.10).

5: 34.12 Physical Applications

… ►The angular momentum coupling coefficients (

\mathit{3j}

\mathit{6j}

, and

\mathit{9j}

symbols) are essential in the fields of nuclear, atomic, and molecular physics. …

6: 14.30 Spherical and Spheroidal Harmonics

… ►In the quantization of angular momentum the spherical harmonics

Y_{{l},{m}}\left(\theta,\phi\right)

are normalized solutions of the eigenvalue equations …Here, in spherical coordinates,

\mathrm{L}^{2}

is the squared angular momentum operator: ►

14.30.12

\mathrm{L}^{2}=-\hbar^{2}\left(\frac{1}{\sin\theta}\frac{\partial}{\partial% \theta}\left(\sin\theta\frac{\partial}{\partial\theta}\right)+\frac{1}{{\sin}^% {2}\theta}\frac{{\partial}^{2}}{{\partial\phi}^{2}}\right),

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Defines:: $\mathrm{L}$ : angular momentum operator (locally)
Symbols:: $\frac{\partial\NVar{f}}{\partial\NVar{x}}$ : partial derivative of $f$ with respect to $x$ , $\,\partial\NVar{x}$ : partial differential of $x$ and $\sin\NVar{z}$ : sine function
Referenced by:: §18.39(ii)
Permalink:: http://dlmf.nist.gov/14.30.E12
Encodings:: pMML, png, TeX
See also:: Annotations for §14.30(iv), §14.30 and Ch.14

►and

\mathrm{L}_{z}

is the

z

component of the angular momentum operator ►

14.30.13

\mathrm{L}_{z}=-\mathrm{i}\hbar\frac{\partial}{\partial\phi};

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Defines:: $\mathrm{L}_{z}$ : $z$ component of the angular momentum operator (locally)
Symbols:: $\mathrm{i}$ : imaginary unit, $\frac{\partial\NVar{f}}{\partial\NVar{x}}$ : partial derivative of $f$ with respect to $x$ , $\,\partial\NVar{x}$ : partial differential of $x$ and $z$ : complex variable
Referenced by:: §14.30(iv), Erratum (V1.1.0) for Additions
Permalink:: http://dlmf.nist.gov/14.30.E13
Encodings:: pMML, png, TeX
Addition (effective with 1.1.0):: This equation was added.
See also:: Annotations for §14.30(iv), §14.30 and Ch.14

…

7: 14.31 Other Applications

… ►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)). …

8: Bibliography T

… ►

T. Tamura (1970) Angular momentum coupling coefficients. Comput. Phys. Comm. 1 (5), pp. 337–342.

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Notes:: Single-precision Fortran
External Links:: Document, Code
Referenced by:: 11st item.
Encodings:: BibTeX

… ►

W. J. Thompson (1994) Angular Momentum: An Illustrated Guide to Rotational Symmetries for Physical Systems. A Wiley-Interscience Publication, John Wiley & Sons Inc., New York.

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Notes:: With 1 Macintosh floppy disk (3.5 inch; DD). Programs for the calculation of $3j,6j,9j$ symbols are included.
External Links:: ISBN 0-471-55264-X, MathReview (J. F. Cornwell), ZentralBlatt
Referenced by:: §34.3(vii).
Encodings:: BibTeX

…

9: Bibliography E

… ►

A. R. Edmonds (1974) Angular Momentum in Quantum Mechanics. 3rd printing, with corrections, 2nd edition, Princeton University Press, Princeton, NJ.

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Notes:: Reprinted in 1996.
External Links:: ISBN 0-691-02589-4, MathReview, ZentralBlatt
Referenced by:: §14.30(i), §14.30(ii), §14.30(iii), §14.30(iv), §14.30(iv), §14.31(iii), (34.1.1), §34.1, §34.1, §34.13, §34.2, §34.3(i), §34.3(i), §34.3(ii), §34.3(iii), §34.3(iv), §34.3(vii), §34.3(vii), §34.4, §34.5(i), §34.5(ii), §34.5(iii), §34.5(iv), §34.5(vi), §34.6, §34.7(i), §34.7(ii), §34.7(iv), §34.7(vi), Ch.34, Erratum (V1.0.14) for Section 34.1, Erratum (V1.0.15) for Section 34.1.
Encodings:: BibTeX

…

10: Bibliography J

… ►

B. R. Judd (1975) Angular Momentum Theory for Diatomic Molecules. Academic Press, New York.

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External Links:: ISBN 0-12-391950-9
Referenced by:: §30.12, §34.12, Profile Brian R. Judd.
Encodings:: BibTeX

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