A pair of [observable](Observable.md)s, $\hat{A}$ and $\hat{B}$ are _compatible_ if they [commute](Commutators%20in%20quantum%20mechanics.md). What this means is that one can measure a quantity associated with [state](State%20vector), $|\psi\rangle$ corresponding with $\hat{A}$ _without_ affecting the measured quantity corresponding with $\hat{B}$ and vice versa. Any set of compatible set of compatible observables forms a [complete sets of compatible operators](Complete%20sets%20of%20compatible%20operators.md) (a CSCO). conversely two observables are _[incompatible](Conjugate%20observables%20in%20quantum%20mechanics.md)_ if they don't commute. %%This entry will be expanded from info largely from Gottfried and Yang's book.%% --- # Proofs and examples ## Proof that compatible observables form a CSCO #QuantumMechanics/QuantumMeasurement/QuantumObservables