- #1

- 1

- 0

## 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..