If \(\rm \hat{L}_x, \hat{L}_y, \hat{L}_z\) are the components of the angular momentum operator in three dimensions the commutator \(\left[\hat{L}_x, \hat{L}_x \hat{L}_y\hat{L}_z\right]\) may be simplified to
1
\(\rm i \hbar L_x\left(\hat{L}_z^2-\hat{L}_y^2\right)\)
2
\(\rm i \hbar \hat{L}_z \hat{L}_y \hat{L}_x\)
3
\(\rm i \hbar L_x\left(2 \hat{L}_z^2-\hat{L}_y^2\right)\)
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0
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