Given a particle of spin 3/2 in the state |3/2, 3/2>, find a quantum operator which rotates this particle by 1 degree around the vector (1,1,1). What is the state after the rotation in |3/2, m> basis?
The Attempt at a Solution
Ok so the operator should be
where the J's are the 4d pauli matrices.
And I get the state in |3/2, m> basis by sandwiching <3/2, m| R |3/2, 3/2>, where
|3/2, 3/2> = \left(
Is this correct? If I do this it seems that I can never get |3/2 -1/2> or |3/2 -3/2> whatever [tex]\alpha[/tex] which looks fishy..