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1: 34.2 Definition: Symbol
§34.2 Definition: Symbol
►The quantities in the symbol are called angular momenta. …They therefore satisfy the triangle conditions …where is any permutation of . The corresponding projective quantum numbers are given by …2: 3.5 Quadrature
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Table 3.5.2: Nodes and weights for the 10-point Gauss–Legendre formula.
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3.5.1
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►In Stenger (1993, Chapter 3) the rule (3.5.5) is considered in the framework of Sinc approximations (§3.3(vi)).
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3.5.7
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0.97390 65285 17171 720 | 0.06667 13443 08688 138 |
3: 34.11 Higher-Order Symbols
§34.11 Higher-Order Symbols
…4: 4.17 Special Values and Limits
5: 34.12 Physical Applications
§34.12 Physical Applications
►The angular momentum coupling coefficients (, , and symbols) are essential in the fields of nuclear, atomic, and molecular physics. …, and symbols are also found in multipole expansions of solutions of the Laplace and Helmholtz equations; see Carlson and Rushbrooke (1950) and Judd (1976).6: 34.3 Basic Properties: Symbol
§34.3 Basic Properties: Symbol
… ►§34.3(ii) Symmetry
… ►§34.3(iv) Orthogonality
… ►§34.3(vi) Sums
… ►7: 34.5 Basic Properties: Symbol
8: 34.4 Definition: Symbol
§34.4 Definition: Symbol
►The symbol is defined by the following double sum of products of symbols: …where the summation is taken over all admissible values of the ’s and ’s for each of the four symbols; compare (34.2.2) and (34.2.3). ►Except in degenerate cases the combination of the triangle inequalities for the four symbols in (34.4.1) is equivalent to the existence of a tetrahedron (possibly degenerate) with edges of lengths ; see Figure 34.4.1. … ►where is defined as in §16.2. …9: 34.1 Special Notation
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►The main functions treated in this chapter are the Wigner symbols, respectively,
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►An often used alternative to the symbol is the Clebsch–Gordan coefficient
…For other notations for , , symbols, see Edmonds (1974, pp. 52, 97, 104–105) and Varshalovich et al. (1988, §§8.11, 9.10, 10.10).