Clebsch–Gordan coefficients

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1: 34.1 Special Notation

… ►An often used alternative to the $\mathit{3}j$ symbol is the Clebsch–Gordan coefficient ►

34.1.1

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Symbols:

: $\mathit{3}j$ 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–Gordancoefficients are an alternative formulation of angular momentum problems, rather than alternative notation for the $\mathit{3}j$. The sign of $m_3$ was changed for clarity.

See also:

Annotations for §34.1 and Ch.34

… ►For other notations for $\mathit{3}j$, $\mathit{6}j$, $\mathit{9}j$ symbols, see Edmonds (1974, pp. 52, 97, 104–105) and Varshalovich et al. (1988, §§8.11, 9.10, 10.10).

2: 34.14 Tables

… ►Biedenharn and Louck (1981) give tables of algebraic expressions for Clebsch–Gordan coefficients and $\mathit{6}j$ symbols, together with a bibliography of tables produced prior to 1975. In Varshalovich et al. (1988) algebraic expressions for the Clebsch–Gordan coefficients with all parameters $\le 5$ and numerical values for all parameters $\le 3$ are given on pp. …

3: 16.24 Physical Applications

… ►

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

►The $\mathit{3}j$ symbols, or Clebsch–Gordan coefficients, play an important role in the decomposition of reducible representations of the rotation group into irreducible representations. …

4: Bibliography K

… ►

Pascal program for generating tables of $\mathrm{SU}(3)$ Clebsch-Gordan coefficients. Comput. Phys. Comm. 85 (1), pp. 82–88.

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External Links:

ISSN 0010-4655, Document, Code, MathReview Entry, ZentralBlatt

Referenced by:

6th item.

Encodings:

BibTeX

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Clebsch-Gordan coefficients for $\mathrm{SU}(2)$ and Hahn polynomials. Nieuw Arch. Wisk. (3) 29 (2), pp. 140–155.

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External Links:

ISSN 0028-9825, MathReview (Jiří Patera), ZentralBlatt

Referenced by:

§18.38(iii).

Encodings:

BibTeX

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5: Bibliography D

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A simple sum formula for Clebsch-Gordan coefficients. Lett. Math. Phys. 5 (3), pp. 207–211.

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External Links:

ISSN 0377-9017, Document, MathReview, ZentralBlatt

Referenced by:

§14.17(iv).

Encodings:

BibTeX

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6: Bibliography L

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New recursion relation for the Clebsch-Gordan coefficients. Phys. Rev. (2) 110 (4), pp. 815–816.

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External Links:

Document, MathReview, ZentralBlatt

Referenced by:

§34.3(iii).

Encodings:

BibTeX

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7: Bibliography S

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Quantum Theory of Angular Momentum: Selected Topics. Springer-Verlag, Berlin.

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Notes:

Fortran programs comparing methods for the calculation of Clebsch–Gordan coefficients, and of $6j$ and $9j$ symbols, are given on pp. 266–292

External Links:

ISBN 3-540-56308-3; 0-387-56308-3, MathReview (A. U. Klimyk), ZentralBlatt

Referenced by:

§34.10, §34.13, §34.15, §34.3(ii), §34.3(iii), §34.5(ii), §34.6.

Encodings:

BibTeX

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8: Errata

… ►

The relation between Clebsch-Gordan and $\mathit{3}j$ symbols was clarified, and the sign of $m_3$ was changed for readability. The reference Condon and Shortley (1935) for the Clebsch-Gordan coefficients was replaced by Edmonds (1974) and Rotenberg et al. (1959) and the references for $\mathit{3}j$, $\mathit{6}j$, $\mathit{9}j$ symbols were made more precise in §34.1.

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The reference for Clebsch-Gordan coefficients, Condon and Shortley (1935), was replaced by Edmonds (1974) and Rotenberg et al. (1959). The references for $\mathit{3}j$, $\mathit{6}j$, $\mathit{9}j$ symbols were made more precise.

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