9-j symbolFrom Wikipedia, the free encyclopedia In physics, Wigner's 9-j symbols were introduced by Eugene Paul Wigner in 1937. They are related to recoupling coefficients in quantum mechanics involving four angular momenta Jucys diagram for the Wigner 9-j symbol. The diagram describes a summation over six 3-jm symbols. Plus signs on each nodes indicate an anticlockwise reading of the lines for the 3-jm symbol, whereas minus signs indicate clockwise. Due to its symmetries, there are many ways in which the diagram can be drawn. ( 2 j 3 + 1 ) ( 2 j 6 + 1 ) ( 2 j 7 + 1 ) ( 2 j 8 + 1 ) { j 1 j 2 j 3 j 4 j 5 j 6 j 7 j 8 j 9 } = ⟨ ( ( j 1 j 2 ) j 3 , ( j 4 j 5 ) j 6 ) j 9 | ( ( j 1 j 4 ) j 7 , ( j 2 j 5 ) j 8 ) j 9 ⟩ . {\displaystyle {\sqrt {(2j_{3}+1)(2j_{6}+1)(2j_{7}+1)(2j_{8}+1)}}{\begin{Bmatrix}j_{1}&j_{2}&j_{3}\\j_{4}&j_{5}&j_{6}\\j_{7}&j_{8}&j_{9}\end{Bmatrix}}=\langle ((j_{1}j_{2})j_{3},(j_{4}j_{5})j_{6})j_{9}|((j_{1}j_{4})j_{7},(j_{2}j_{5})j_{8})j_{9}\rangle .}
In physics, Wigner's 9-j symbols were introduced by Eugene Paul Wigner in 1937. They are related to recoupling coefficients in quantum mechanics involving four angular momenta Jucys diagram for the Wigner 9-j symbol. The diagram describes a summation over six 3-jm symbols. Plus signs on each nodes indicate an anticlockwise reading of the lines for the 3-jm symbol, whereas minus signs indicate clockwise. Due to its symmetries, there are many ways in which the diagram can be drawn. ( 2 j 3 + 1 ) ( 2 j 6 + 1 ) ( 2 j 7 + 1 ) ( 2 j 8 + 1 ) { j 1 j 2 j 3 j 4 j 5 j 6 j 7 j 8 j 9 } = ⟨ ( ( j 1 j 2 ) j 3 , ( j 4 j 5 ) j 6 ) j 9 | ( ( j 1 j 4 ) j 7 , ( j 2 j 5 ) j 8 ) j 9 ⟩ . {\displaystyle {\sqrt {(2j_{3}+1)(2j_{6}+1)(2j_{7}+1)(2j_{8}+1)}}{\begin{Bmatrix}j_{1}&j_{2}&j_{3}\\j_{4}&j_{5}&j_{6}\\j_{7}&j_{8}&j_{9}\end{Bmatrix}}=\langle ((j_{1}j_{2})j_{3},(j_{4}j_{5})j_{6})j_{9}|((j_{1}j_{4})j_{7},(j_{2}j_{5})j_{8})j_{9}\rangle .}