View source for Matrix Elements and the Wigner Eckhart Theorem Example

Let <math> \vec J_1 </math> and <math> \vec J_2 </math> be two angular momentum operators, <math> \vec J = \vec J_1 + \vec J_2 </math> is the sum of these two vectors, and <math> |J M \rangle </math> denotes the eigen states of <math> \vec J^2 </math> and <math> \bold J _z </math>.

Show that the matrix elements of <math> J_1^- , \langle J M | J_1^- | J' (M + 1)\rangle </math>, unless <math> \bold J' = \bold J </math> or <math> \bold J' = \bold J \pm 1 </math>.