Racah W-Coefficient

The Racah W-coefficients, sometimes simply called the Racah coefficients (Shore and Menzel 1968, p. 279), are quantities introduced by Racah (1942) that are related to the Clebsch-Gordan coefficients by




The Racah W-coefficients are related to the Wigner 6j-symbols by

 (-1)^(a+b+c+d)W(abcd;ef)={a b c; d e f}

(Messiah 1962, p. 1062; Shore and Menzel 1968, p. 279).

See also

Clebsch-Gordan Coefficient, Racah V-Coefficient, Wigner 3j-Symbol, Wigner 6j-Symbol, Wigner 9j-Symbol

Explore with Wolfram|Alpha


Biedenharn, L. C. and Louck, J. D. The Racah-Wigner Algebra in Quantum Theory. Reading, MA: Addison-Wesley, 1981.Biedenharn, L. C. and Louck, J. D. Angular Momentum in Quantum Physics: Theory and Applications. Reading, MA: Addison-Wesley, 1981.Messiah, A. "Racah Coefficients and '6j' Symbols." Appendix C.II in Quantum Mechanics, Vol. 2. Amsterdam, Netherlands: North-Holland, pp. 1061-1066, 1962.Racah, G. "Theory of Complex Spectra. II." Phys. Rev. 62, 438-462, 1942.Shore, B. W. and Menzel, D. H. Principles of Atomic Spectra. New York: Wiley, 1968.Sobel'man, I. I. "Angular Momenta." Ch. 4 in Atomic Spectra and Radiative Transitions, 2nd ed. Berlin: Springer-Verlag, 1992.

Referenced on Wolfram|Alpha

Racah W-Coefficient

Cite this as:

Weisstein, Eric W. "Racah W-Coefficient." From MathWorld--A Wolfram Web Resource.

Subject classifications