It is not as intuitive for perturbed observables, since its familiar form assumes that the operator corresponding to the observable in question is not explicitly time dependent.
This relation may be most directly derived by noting the commutation of the time derivative and bra-ket operators, then assuming harmonic time dependence for the solution of the time-dependent Schr?dinger equation. It is not as intuitive for perturbed observables, since its familiar form assumes that the operator corresponding to the observable in question is not explicitly time dependent. A demonstration of the Bohr correspondence principle, it is most often cited for the case of the momentum observable in the coordinate representation, in which case it reduced to a highly familiar statement about the total time derivative of the momentum's expectation. FTP, name this theorem, often cited as a quantum analog of Newton's 2nd law.
This relation may be most directly derived by noting the commutation of the time derivative and bra-ket operators, then assuming harmonic time dependence for the solution of the time-dependent Schr?dinger equation.
Ehrenfest's theorem