# Construct an Operator (2-D QM)

Gold Member

## Homework Statement

Construct the $$S_r$$ 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 $$S_r$$ will do to a state |s m>

I thought about looking at the fact that:

$$x = rsin(\theta)cos(\phi), y = rsin(\theta)cos(\phi), and z=rcos(\theta)$$

and just replace all the x's with $$S_x$$'s and r's with $$S_r$$'s etc. But I don't think this will work as it will give me 3 different answers.