This is a table of Clebsch–Gordan coefficients used for adding angular momentum values in quantum mechanics. The overall sign of the coefficients for each set of constant , , is arbitrary to some degree and has been fixed according to the Condon–Shortley and Wigner sign convention as discussed by Baird and Biedenharn. Tables with the same sign convention may be found in the Particle Data Group's Review of Particle Properties and in online tables. Formulation The Clebsch–Gordan coefficients are the solutions to Explicitly: The summation is extended over all integer for which the argument of every factorial is nonnegative. For brevity, solutions with and are omitted. They may be calculated using the simple relations and Specific values The Clebsch–Gordan coefficients for j values less than or equal to 5/2 are given below. When , the Clebsch–Gordan coefficients are given by . SU(N) Clebsch–Gordan coefficients Algorithms to produce Clebsch–Gordan coefficients for higher values of and , or for the su(N) algebra instead of su(2), are known. A web interface for tabulating SU(N) Clebsch–Gordan coefficients is readily available. References External links Online, Java-based Clebsch–Gordan Coefficient Calculator by Paul Stevenson Other formulae for Clebsch–Gordan coefficients. Web interface for tabulating SU(N) Clebsch–Gordan coefficients Representation theory of Lie groups Clebsch–Gordan coefficients