- #1

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[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?