Thus, one may express the values of | α | and | β | in terms of the eigenvalues of J and J z : | α α | 2 = ℏ ℏ 2 j ( j + 1 ) − − ℏ ℏ 2 m 2 − − ℏ ℏ 2 m = ℏ ℏ 2 ( j − − m ) ( j + m + 1 ) , | β β | 2 = ℏ ℏ 2 j ( j + 1 ) − − ℏ ℏ 2 m 2 + ℏ ℏ 2 m = ℏ ℏ 2 ( j + m ) ( j − − m + 1 ) .