# Angular momentum and Expectation values

1. Nov 15, 2009

### Ben4000

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

Express Lx in terms of the commutator of Ly and Lz and, using this result, show that <Lx>=0 for this particle.

3. The attempt at a solution

[Ly,Lz]=i(hbar)Lx

<Lx>=< l,m l Lx l l,m>

then what?

2. Nov 15, 2009

### Ben4000

I can show that <Lx>=0 using the ladder opertators, but i dont think this is what is wanted from this question... how do i use
[Ly,Lz]=i(hbar)Lx to prove <Lx> = 0?

3. Nov 16, 2009

### gabbagabbahey

$$\langle L_x\rangle=\langle l,m|L_x|l,m\rangle=\frac{-i}{\hbar}\langle l,m|[L_y,L_z]|l,m\rangle$$

Expand the commutator using its definition, and take the hermitian conjugate of the resulting equation...what do you see?