Rotation commutators for orbital angular momentum
= Rotation commutators for orbital angular momentum
For $L_i=\varepsilon_{ik\ell}X_kP_\ell$ and $[X_i,P_j]=i\hbar\delta_{ij}$,
$$
[L_i,X_j]=i\hbar\varepsilon_{ijk}X_k,
\qquad
[L_i,P_j]=i\hbar\varepsilon_{ijk}P_k.
$$