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Quantum rotation operator question

  • Thread starter trulio
  • Start date
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Homework Statement


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?

Homework Equations





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..
 

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