Question

The three matrix operators for spin one satisfy s_xs_y - s_ys_x = is_z and cyclic permutations. Show that

\(s_z^3 = s_z,(s_x \pm is_y)^3 = 0\).

Answer 1

The matrix forms of the spin angular momentum operator (s = 1) in the (s², s,) representation, in which s², s, are diagonal, are