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I need help with commutators

  1. Feb 21, 2013 #1
    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:
    [tex] [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)[/tex]
    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:
    [tex][L_x, L_y] = yp_x[p_z, z] + xp_y[z, p_z][/tex]
    How is Griffiths able to factor out the [itex] yp_x \text{ and } xp_y[/itex]? When I expand eqn (1), I get:
    [tex] [L_x, L_y] = yp_zzp_x-zp_xyp_z + zp_yxp_z - xp_zzp_y [/tex]
    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



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    3. The attempt at a solution
     
  2. jcsd
  3. Feb 21, 2013 #2
    Oh, never mind. I think I can commute momentum and position operators acting on different variables. So [itex] xp_z = p_zx [/itex].
     
  4. Feb 21, 2013 #3

    vela

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    That's right.
     
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