How does the author go from the end of this step:
To the first step here:
This is from Griffiths, Introduction to Quantum Mechanics, 2nd Edition, pgs. 160-161. I don't understand how he is using the canonical commutation relations.
2026-04-02 04:28:57.1775104137
How does the author go from this step to the next in proving angular momentum commutation relation?
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The middle two terms in the bottom line of the top equation are $0$ as explained in the displayed paragraph below. That leaves computing \begin{align} [yp_z,zp_x]&=yp_zzp_x-zp_xyp_z\\ &=yp_xp_zz-yp_xzp_z\\ &=yp_x(p_zz-zp_z)\\ &=yp_x[p_z,z] \end{align} and similarly for the other term. Note that I am using the fact that $y$ and $p_x$ commute with each other and with both $p_z$ and $z$.