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Racah V-Coefficient

The Racah V-coefficients are written

V(j_1j_2j;m_1m_2m)
(1)

and are sometimes expressed using the related Clebsch-Gordan coefficients

C_(m_1m_2)^j=(j_1j_2m_1m_2|j_1j_2jm),
(2)

or Wigner 3j-symbols. Connections among the three are

(j_1j_2m_1m_2|j_1j_2m)=(-1)^(-j_1+j_2-m)sqrt(2j+1)(j_1 j_2 j; m_1 m_2 -m)
(3)
(j_1j_2m_1m_2|j_1j_2jm)=(-1)^(j+m)sqrt(2j+1)V(j_1j_2j;m_1m_2-m)
(4)
V(j_1j_2j;m_1m_2m)=(-1)^(-j_1+j_2+j)(j_1 j_2 j_1; m_2 m_1 m_2).
(5)

See also

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

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References

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.Sobel'man, I. I. "Angular Momenta." Ch. 4 in Atomic Spectra and Radiative Transitions, 2nd ed. Berlin: Springer-Verlag, 1992.

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Racah V-Coefficient

Cite this as:

Weisstein, Eric W. "Racah V-Coefficient." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RacahV-Coefficient.html

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