# Quantum rotation operator question

1. Apr 4, 2009

### trulio

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

3. The attempt at a solution
Ok so the operator should be
$1- \frac{i\alpha}{\sqrt{3}h}(J_1+J_2+J_3)$
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

$$|3/2, 3/2> = \left( \begin{array}{cc} 1\\ 0\\ 0\\ 0\\ \end{array} \right)$$
etc
Is this correct? If I do this it seems that I can never get |3/2 -1/2> or |3/2 -3/2> whatever $$\alpha$$ which looks fishy..

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