Wigner 3j-Symbol

The Wigner symbols are written

(1)

(2)

(3)

(4)

(5)

(6)

			(7)

(8)

(9)

General formulas are very complicated, but some specific cases are

	(10)

	(11)

(12)

For Spherical Harmonics ,

	(13)

	(14)

(15)

References

Abramowitz, M. and Stegun, C. A. (Eds.). ``Vector-Addition Coefficients.'' §27.9 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 1006-1010, 1972.

Condon, E. U. and Shortley, G. The Theory of Atomic Spectra. Cambridge, England: Cambridge University Press, 1951.

de Shalit, A. and Talmi, I. Nuclear Shell Theory. New York: Academic Press, 1963.

Gordy, W. and Cook, R. L. Microwave Molecular Spectra, 3rd ed. New York: Wiley, pp. 804-811, 1984.

Messiah, A. ``Clebsch-Gordan (C.-G.) Coefficients and `' Symbols.'' Appendix C.I in Quantum Mechanics, Vol. 2. Amsterdam, Netherlands: North-Holland, pp. 1054-1060, 1962.

Rotenberg, M.; Bivens, R.; Metropolis, N.; and Wooten, J. K. The and Symbols. Cambridge, MA: MIT Press, 1959.

Shore, B. W. and Menzel, D. H. Principles of Atomic Spectra. New York: Wiley, pp. 275-276, 1968.

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

Wigner, E. P. Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra, expanded and improved ed. New York: Academic Press, 1959.

• Whole Number
• Width (Partial Order)
• Width (Size)
• Wiedersehen Manifold
• Wieferich Prime
• Wielandt's Theorem
• Wiener Filter
• Wiener Function
• Wiener-Khintchine Theorem
• Wiener Measure
• Wiener Space
• Wigner 3j-Symbol
• Wigner 6j-Symbol
• Wigner 9j-Symbol
• Wigner-Eckart Theorem
• Wilbraham-Gibbs Constant
• Wilcoxon Rank Sum Test
• Wilcoxon Signed Rank Test
• Wild Knot
• Wild Point
• Wilf-Zeilberger Pair
• Wilkie's Theorem
• Williams p+1 Factorization Method
• Wilson Plug
• Wilson Prime