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.[1] Tables with the same sign convention may be found in the Particle Data Group's Review of Particle Properties[2] and in online tables.[3]
Formulation
The Clebsch–Gordan coefficients are the solutions to
Explicitly:
The summation is extended over all integer k for which the argument of every factorial is nonnegative.[4]
For brevity, solutions with m < 0 and j1 < j2 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.[5]
j2 = 0
When j2 = 0, the Clebsch–Gordan coefficients are given by .
^Baird, C.E.; L. C. Biedenharn (October 1964). "On the Representations of the Semisimple Lie Groups. III. The Explicit Conjugation Operation for SUn". J. Math. Phys. 5 (12): 1723–1730. Bibcode:1964JMP.....5.1723B. doi:10.1063/1.1704095.
^Alex, A.; M. Kalus; A. Huckleberry; J. von Delft (February 2011). "A numerical algorithm for the explicit calculation of SU(N) and SL(N,C) Clebsch–Gordan coefficients". J. Math. Phys. 82: 023507. arXiv:1009.0437. Bibcode:2011JMP....52b3507A. doi:10.1063/1.3521562.
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