Wigner Symbols

Wigner, Clebsch-Gordan, Racah, and Gaunt coefficients

Collection of functions for calculating Wigner 3j, 6j, 9j, Clebsch-Gordan, Racah as well as Gaunt coefficients exactly, all evaluating to a rational number times the square root of a rational number [Rasch03].

Please see the description of the individual functions for further details and examples.



‘Symmetry Properties of Clebsch-Gordan Coefficients’, T. Regge, Nuovo Cimento, Volume 10, pp. 544 (1958)


‘Symmetry Properties of Racah Coefficients’, T. Regge, Nuovo Cimento, Volume 11, pp. 116 (1959)


A. R. Edmonds. Angular momentum in quantum mechanics. Investigations in physics, 4.; Investigations in physics, no. 4. Princeton, N.J., Princeton University Press, 1957.


J. Rasch and A. C. H. Yu, ‘Efficient Storage Scheme for Pre-calculated Wigner 3j, 6j and Gaunt Coefficients’, SIAM J. Sci. Comput. Volume 25, Issue 4, pp. 1416-1428 (2003)


‘FORTRAN program for the integral of three spherical harmonics’, A. Liberato de Brito, Comput. Phys. Commun., Volume 25, pp. 81-85 (1982)