Formula: Commutator Between Angular Momentum Squared and Angular Momentum Component Angular momentum component Squared angular momentum
$$[ L^2, \, L_j ] ~=~ 0$$
Angular momentum component
$$ L_j $$ Unit $$ \mathrm{Js} $$
This is an angular momentum operator, namely the \(j\)th component of the angular momentum vector operator \( \boldsymbol{L} \), i.e. \(L_{\text x}\), \(L_{\text y}\) or \(L_{\text z}\).
Squared angular momentum
$$ L^2 $$
Angular momentum operator is given by:
$$ L^2 ~=~ L_{\text x}^2 ~+~ L_{\text y}^2 ~+~ L_{\text z}^2 $$
Since \(L^2\) commutates with all angular momentum components, they have the same eigenstates.