Question 7. Addition of Angular Momenta. [10] Consider two angular momenta J1 and J2 The state vectors for the two angular momenta are elements of their respective Hilbert spaces, say, .931 and 9%. The Hilbert space of the joint system of the two angular momenta is given by 1%\":'991 {23%. There are two sets of basis vectors for 33': one set with the eigenstates of J12, J22 ,J1 , and J2 and the other set with the eigenstates of Jf, J3, J2, and J2. The relation between the two sets of eigenstates is given by |j1m>= 22011j2;m11m2|j1m>|31,3'2;m1,m2)- m1 m2 Consider now the case of J1 = E with E = 2, and J2 = 5' with s = 1/2. Apply the above relation for the smallest value of j, i.e., give all the allowed expansions for |j,m) in terms of the \"1,552; m1,m2) for the smallest value of j