In the book Quantum Mechanics volume 2 by Cohen-Tannoudji, in Electric dipole approximation, it was written that $\left[\boldsymbol{Z}, H_0\right]=i \hbar \frac{\partial H_0}{\partial P_{\boldsymbol{z}}}$ where $H_0=\frac{P^2}{2m}+V(R)$, $V(R)$ is the central potential. How to derive this commutation?
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![$\left[\boldsymbol{Z}, H_0\right]=i \hbar \frac{\partial H_0}{\partial P_{\boldsymbol{z}}}$](https://i.stack.imgur.com/De9g0.jpg){kind=link}
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1see the answers in https://physics.stackexchange.com/q/139142 – Diego Nov 08 '23 at 18:53
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@Diego thank you – Lusypher Nov 08 '23 at 19:45
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1Does this answer your question? How to derive $[x_i, F(\vec p)] = i \hbar \frac {\partial F(\vec p)}{\partial p_i}$ – CPlus Nov 08 '23 at 21:15