- #1

Matterwave

Science Advisor

Gold Member

- 3,965

- 326

## Homework Statement

Construct the [tex]S_r[/tex] operator, which is the spin operator in the r direction.

## Homework Equations

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.