Sequential measurements and the commutator

The commutator of two operators, defined as $[A,B]≡AB−BA$⁠, plays an important role in quantum mechanics. Two relationships derived in nearly all undergraduate texts are

and the time evolution of the expectation value of an observable $A$

where $∣ψ⟩$ is the state of the system, $H$ is the Hamiltonian operator, and $ΔA$ is the uncertainty in $A$⁠. The operators $A$ and $B$ correspond to the observables $A$ and $B$⁠....