In our discussion of the Wigner-Eckart theorem, we obtained the reduced matrix element for the angular momentum operator: ⟨j′k′∥J∥j′′k′′⟩. This required knowing the Clebsch-Gordan coefficient C(1,j,j;0,m,m). By using the general prescription for calculating the 3j symbols we developed, calculate the 3j symbol
(10jmj−m),
and hence obtain C(1,j,j;0,m,m).