Therefore, for the complete system, the set of eigenvalues { j 1 , m 1 , j 2 , m 2 } completely specifies a unique basis state, and { J 1 2 , J 1 z , J 2 2 , J 2 z } forms a CSCO. Equivalently, there exists another set of basis states for the system, in terms of the total angular momentum operator J = J 1 + J 2 . The eigenvalues of J 2 are j ( j + 1 ) ℏ ℏ 2 where j takes on the values j 1 + j 2 , j 1 + j 2 − − 1 , . . . , | j 1 − − j 2 | , and those of J z are m where m = − − j , − − j + 1 , . . . j − − 1 , j . The basis states of the operators J 2 and J z are | j 1 j 2 ; j m ⟩ ⟩ . Thus we may also specify a unique basis state in the Hilbert space of the complete system by the set of eigenvalues { j 1 , j 2 , j , m } , and the corresponding CSCO is { J 1 2 , J 2 2 , J 2 , J z } .