They are employed in vector coupling for the three dimensional rotation group SO(3) where they have a high degree of symmetry since SO(3) is a simply reducible group. In representation theory, they can be defined as the elements of the matrix reducin
They are employed in vector coupling for the three dimensional rotation group SO(3) where they have a high degree of symmetry since SO(3) is a simply reducible group. In representation theory, they can be defined as the elements of the matrix reducing the direct product of two irreducible representations of compact Lie groups. Generalizations include Racah coefficients or Wigner 6j and 9j symbols, for cases in which the integral product of greater than three spherical harmonics are desired. They can be computed by expressing a product of two spherical harmonics as a sum of individual spherical harmonics. For 10 points, name these numbers that are commonly employed to obtain the coupling amplitude between uncoupled and coupled representations of angular momenta in quantum mechanics.
They are employed in vector coupling for the three dimensional rotation group SO(3) where they have a high degree of symmetry since SO(3) is a simply reducible group.
Clebsch-Gordan coefficients [or Wigner 3j coefficient]