This paper considers in detail numerical methods of solving Laplace's equation in an arbitrary two-dimensional region with given boundary values. The methods involve the solution of approximating difference equations by iterative procedures. Modifications of the standard Liebmann procedure are developed which lead to a great increase in the convenience and rapidity of obtaining such a numerical solution. These modifications involve the use of formulas which simultaneously improve a block of points in place of a single point; methods of operating on the differences of trial functions in place of the functions themselves; and also a method of extrapolating to the final solution of the difference equations. The theory underlying these procedures is considered in detail by a new method which involves the expansion of the error and difference functions in terms of eigenfunctions. This permits definite comparison of rates of convergence of various procedures. The techniques of handling practical problems are considered in detail.
The 3-J and 6-J Symbols The MIT Press 3j-6j-and 9j-symbols. The Clebsch-Gordan coefficients obey certain symmetry relations, like. ?j1j2 m1m2j1j2 jm?. = (?1)j1+j2?j?j2j1 m2m1j2j1 jm?. Catalog Record: The 3-j and 6-j symbols Hathi Trust Digital Library Abstract. We present an efficient implementation for the evaluation of Wigner 3j, 6j, and 9j symbols. These represent numerical transformation coefficients that U111 Wigner 3-j, 6-j, 9-j Symbols Clebsch-Gordan, Racah W .-CMD Figure 34.2.1: Angular momenta j_r and projective quantum numbers m_ Figure 34.4.1: Tetrahedron corresponding to 6j symbol. Notation. 34.1 Special Images for The 3-J and 6-J Symbols 31 May 2002. Summary. This chapter contains sections titled: Introduction. Clebsch-Gordan coefficients. Wigner 3?j symbols. Wigner 6?j symbols. Reference. Semiclassical Mechanics of the Wigner 6j-Symbol For further information on these symbols, check out their respective Wikipedia pages: 3-j, 6-j and 9-j. For a calculator that can give exact values (not floating point DLMF: 34 3j, 6j, 9j Symbols 1062), commonly simply called the 6j-symbols, are a generalization of Clebsch-Gordan coefficients and Wigner 3j-symbol that arise in the coupling of three. Simplified recursive algorithm for Wigner 3j and 6j symbols. The 3-J and 6-J Symbols.
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