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Quantum rotation operator question

  1. Apr 4, 2009 #1
    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
    [itex]1- \frac{i\alpha}{\sqrt{3}h}(J_1+J_2+J_3)[/itex]
    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

    [tex]
    |3/2, 3/2> = \left(
    \begin{array}{cc}
    1\\
    0\\
    0\\
    0\\
    \end{array}
    \right)

    [/tex]
    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 [tex]\alpha[/tex] which looks fishy..
     
  2. jcsd
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