Show that the (mathrm{SO}(3)) Clebsch-Gordan coefficients (leftlangle j_{1} m_{1} j_{2} m_{2} mid J M ight angle) evaluate to (-1)j-m jmj'm'| 00): = 2j+1 djj' dm,-m'>

Show that the \(\mathrm{SO}(3)\) Clebsch-Gordan coefficients \(\left\langle j_{1} m_{1} j_{2} m_{2} \mid J M\right\rangle\) evaluate to

(-1)j-m jmj'm'| 00): = 2j+1 djj' dm,-m'> for the special case J = M = 0.