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.
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