# Angular Momentum Eigenstate

1. Oct 18, 2011

### atomicpedals

1. The problem statement, all variables and given/known data

The square angular momentum L2 and the z-component Lz of a free particle are measured. They are found to be L2=6$\hbar^2$ and Lz=$\hbar$

What is the state |l,m> of the system after measurement?

2. Relevant equations

L2|l,m>=$\hbar^2$l|l,m>
Lz|l,m>=$\hbar$m|l,m>

3. The attempt at a solution

Is this simply:

L2|lm>=$\hbar^2$l|l,m>=6$\hbar^2$|6,m>
Lz|l,m>=$\hbar$m|l,m>=$\hbar$|l,1>

|l,m> = |6,1> ?

2. Oct 18, 2011

### atomicpedals

I'm getting some contradiction from my notes, the other way I see it the eigenstates could be |2,1>.

3. Oct 18, 2011

### vela

Staff Emeritus
It's $\vert 2 ~ 1 \rangle$. Your first "relevant equation" is incorrect.

4. Oct 18, 2011

### atomicpedals

Cool, means page two of my notes needs a quick correction. Thanks!

5. Oct 18, 2011

### atomicpedals

As a follow up to see if I'm slowly catching on; would the expectation value for Lx then be given by <lm|Lx|lm>?

6. Oct 18, 2011

### vela

Staff Emeritus
Yes.