Classical equations from Ehrenfest theorem
= Classical equations from Ehrenfest theorem
For $H=p^2/(2m)+U(x)$, the <canonical commutation relation> gives
$$
m\frac d{dt}\langle x\rangle=\langle p\rangle,
\qquad
\frac d{dt}\langle p\rangle=-\langle U'(x)\rangle,
\qquad
\frac d{dt}\langle H\rangle=0.
$$
These are the expectation-value analogues of <Newton's second law> and conservation of energy.