SET 1

1. Consider two particles with total spin J_{1}=3/2
and J_{2}=1. Write down all the possible states for the system of these
two particles in terms of J_{1}, J_{1z}, J_{2}, J_{2z.}
Write down all the possible states for the system of these two particles in
terms the total angular momentum J_{tot}, J_{totz}, J_{1},
J_{2.}

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2. Find the rotation matrices that will rotate an object around the x,y,z axes.

3. Express the angular momentum operators as matrices that operate on states of spin 1 and spin 1/2.

4. Discuss one interesting point about spin, rotation, and/or operators.