We consider the case of two systems, 1 and 2, with respective angular momentum operators J 1 and J 2 . We can write the eigenstates of J 1 2 and J 1 z as | j 1 m 1 ⟩ ⟩ and of J 2 2 and J 2 z as | j 2 m 2 ⟩ ⟩ .