I am reading a proof of why(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \left[ \hat{L}_x, \hat{L}_y \right ] = i \hbar \hat{L}_z [/tex]

Given a wavefunction [itex]\psi[/itex],

[tex] \hat{L}_x, \hat{L}_y \psi = \left( -i\hbar \right)^2 \left( y \frac{\partial}{\partial z} - z \frac {\partial}{\partial y} \right ) \left (z \frac{\partial \psi}{\partial x} - x \frac{\partial \psi}{\partial z } \right )[/tex]

[tex]= -\hbar ^2 \left ( yz \frac{\partial ^2 \psi}{\partial z \partial x} + y \frac{\partial \psi}{\partial x} - yx \frac{\partial ^2 \psi}{\partial z^2} - z^2 \frac{\partial ^2 \psi}{\partial y \partial x} + zx \frac{\partial ^2 \psi}{\partial y \partial z} \right )[/tex]

This is a simple expansion of the brackets. I don't understand however, where the second term in the brackets of the last equation comes from?

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# I Angular momentum operator commutation relation

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