# I need help with commutators

1. Feb 21, 2013

### Bobbo Snap

I'm having a lot of trouble following Griffith's quantum mechanics text. I'm in section 4.3 which discusses angular momentum using commutators. The text proceeds as follows:
$$[L_x, L_y] = [yp_z - zp_y, zp_x - xp_z]\\ =[yp_z, zp_x] - [yp_z, xp_z] - [zp_y, zp_x] + [zp_y, xp_z]\\ =[yp_z, zp_x] + [zp_y, xp_z] \qquad (1)$$
Ok, I follow the previous, the last step drops the two middle terms because they do commute. It's the next step I don't get:
$$[L_x, L_y] = yp_x[p_z, z] + xp_y[z, p_z]$$
How is Griffiths able to factor out the $yp_x \text{ and } xp_y$? When I expand eqn (1), I get:
$$[L_x, L_y] = yp_zzp_x-zp_xyp_z + zp_yxp_z - xp_zzp_y$$
I don't see how he can factor those out without commuting position operators with momentum operators which you can't do, right?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 21, 2013

### Bobbo Snap

Oh, never mind. I think I can commute momentum and position operators acting on different variables. So $xp_z = p_zx$.

3. Feb 21, 2013

### vela

Staff Emeritus
That's right.