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A particle has orbital angular momentum given by the quantum number /= 3 and spin angular momentum given by the quantum number s =

 

A particle has orbital angular momentum given by the quantum number /= 3 and spin angular momentum given by the quantum number s = 1. (a) How many distinct states are there with different values for the z components of the orbital and spin angular momenta? (b) What are the possible values for the quantum number j that describes the total angular momentum of the particle? (c) How many distinct states are there with different values for the magni- tude and z component of total angular momentum? (Note that the rules for the addition of angular momenta given by Eq. (8.6) are such that, when angular momenta with quantum numbers and s are combined to give total angular momenta with quantum numbers j=l+s,l+8-1, ...-s, then the number of distinct states with differ- ent values for my and m, is equal to the number of distinct states with different values for j and mj.)

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