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Formula Commutator Between Angular Momentum Squared and Angular Momentum Component Angular momentum component    Squared angular momentum

Formula
Formula: Commutator Between Angular Momentum Squared and Angular Momentum Component
Angular momentum - space-quantization

Angular momentum component

Unit
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

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.