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(Solved): [10] Question 7. Addition of Angular Momenta. Consider two angular momenta and . The st ...



[10]
Question 7. Addition of Angular Momenta.
Consider two angular momenta ?? and ??. The state vectors for the two angular m

[10] Question 7. Addition of Angular Momenta. Consider two angular momenta ?? and ??. The state vectors for the two angular momenta are elements of their respective Hilbert spaces, say, H? and H?. The Hilbert space of the joint system of the two angular momenta is given by H = H? H?. There are two sets of basis vectors for H: one set with the eigenstates of 1, 2, ???, and ?2, and the other set with the eigenstates of 2, ?², ?², and ??. The relation between the two sets of eigenstates is given by |j, m) = ?Xi1, j2; m1, m2|j, m)|j1, j2; m1, m2). m? m2 Consider now the case of ?? = Î with l = 2, and ?? = ? 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 j1, j2; m?, m?) for the smallest value of j.


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