Consider the unit vector n = (i + j + k)/?3 where i, j and k
are the unit vectors in the x, y and z directions.
(a) Construct the spin operator $S_n$ for the component of the spin in the n direction.
(b) Construct the rotation operator $R(\phi)$ for rotations with respect to the n axis, as a 2x2 matrix.
(c) Rotate the $| \frac{1}{2} \frac{1}{2} \rangle$ spin state with respect to the n axis by $2\pi/3$, $4\pi/3$ and $2\pi$.
Interpret your results.