# Commuting observables

1. Mar 18, 2016

### nmsurobert

1. The problem statement, all variables and given/known data
A particle is in a state described by a wave function of the form ψ(r) = (x+y+z)f(r).
What are the values that a measurement of L2 can yield? What is probability for all these results?

2. Relevant equations

3. The attempt at a solution
I feel this problem shouldn't be too hard but I've been struggling with quantum since last semester so any guidance would be nice. I think i should probably write the function in spherical terms to start off with. but I'm not too clear on where to go from there. I also know that i need to use Ylm too but again, I'm pretty confused.

2. Mar 18, 2016

### blue_leaf77

It will be helpful to use the spherical harmonics written in Cartesian coordinates. Your task is to find $Y_{lm}$'s in which the given $\psi(\mathbf{r})$ is expanded, $$\psi(\mathbf{r}) = f(r)\sum_{lm} c_{lm} Y_{lm}(\hat{r})$$

3. Mar 18, 2016

### nmsurobert

ok ill try to do some work with that. I'm still pretty lost on what the whole Ylm thing is about but hopefully i can make some sense of it.

4. Mar 19, 2016

### Megaquark

I don't know what book you're studying out of, but most go through the steps to show that L2Ψ=ħ2l(l+1)Ψ That might help make the problem a bit easier.