I need help with commutators

  • Thread starter Bobbo Snap
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  • #1
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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?

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Answers and Replies

  • #2
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Oh, never mind. I think I can commute momentum and position operators acting on different variables. So [itex] xp_z = p_zx [/itex].
 
  • #3
vela
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That's right.
 

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