Hence, a set of coupled eigenstates exist for the total angular momentum operator as well, J 2 | [ j 1 j 2 ] J M ⟩ ⟩ = ℏ ℏ 2 J ( J + 1 ) | [ j 1 j 2 ] J M ⟩ ⟩ J z | [ j 1 j 2 ] J M ⟩ ⟩ = ℏ ℏ M | [ j 1 j 2 ] J M ⟩ ⟩ for M ∈ {− J, − J + 1,..., J }. Note that it is common to omit the [ j 1 j 2 ] part.