Consider addition of two angular momenta J = J1 + J2 , with j1=j2=1. Find the eigenstates of the total angular momentum I jm > in terms of the product states I j1 m1 j2 m2 > in two ways (a) Make use of the tables of the Clebech _Gordan coefficients (b) The state with m1 = m2 = 1 must be a state with j = m = 2 (why?). Apply J- repeatedly to this state to obtain all other states of j = 2. Form an appropriate linear combination of the two states with m1 + m2 =1 to obtain the state with j =1 , and m =1 . Find the other j = 1 states by applying J- repeatedly. Finally, find the j = m = 0 state by forming an appropriate linear combination of the three states with m1 + m2 = 0. (c) Compare the results in (a) and (b). I don't know how to use Clebech - Gordand coefficients, so please explain details using the table.