Construct the [tex]S_r[/tex] operator, which is the spin operator in the r direction.
The pauli-matrices are useful, I would assume.
The Attempt at a Solution
So, the way we constructed the other 3 operators by noting their effects on a state |s m>
But I can't do that here because I have no idea what this operator [tex]S_r[/tex] will do to a state |s m>
I thought about looking at the fact that:
[tex] x = rsin(\theta)cos(\phi), y = rsin(\theta)cos(\phi), and z=rcos(\theta)[/tex]
and just replace all the x's with [tex]S_x[/tex]'s and r's with [tex]S_r[/tex]'s etc. But I don't think this will work as it will give me 3 different answers.
I need help on how to start with this.