Wigner 9j-Symbol
A generalization of Clebsch-Gordan Coefficients and Wigner3j-Symbol and Wigner 6j-Symbol which arises in the coupling of four angular momenta and canbe written in terms of the Wigner 3j-Symbol and Wigner 6j-Symbol.Let tensor operators 
and 
act, respectively, on subsystems 1 and 2. Then the reduced matrix elementof the product 
of these two irreducible operators in the coupled representation is givenin terms of the reduced matrix elements of the individual operators in the uncoupled representation by
 | |
 | |
 | (1) |
is a Wigner 
-symbol(Gordy and Cook 1984).Shore and Menzel (1968) give the explicit formulas
 | |
 | (2) |
 | (3) |
 | (4) |
References
Gordy, W. and Cook, R. L. Microwave Molecular Spectra, 3rd ed. New York: Wiley, pp. 807-809, 1984. Messiah, A. ``` Shore, B. W. and Menzel, D. H. Principles of Atomic Spectra. New York: Wiley, pp. 279-284, 1968.' Symbols.'' Appendix C.III in Quantum Mechanics, Vol. 2. Amsterdam, Netherlands: North-Holland, pp. 567-569 and 1066-1068, 1962.
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