= Solution
For a particle in the scalar <potential energy> $U(x)$,
$$
H=\frac{p^2}{2m}+U(x).
$$
The <canonical commutation relation> $[x,p]=i\hbar$ gives
$$
[H,x]=\frac1{2m}[p^2,x]=-\frac{i\hbar}{m}p.
$$
The <Ehrenfest theorem> with $O=x$ therefore gives
$$
\boxed{m\frac d{dt}\langle x\rangle_\psi=\langle p\rangle_\psi}.
$$
Since $[p^2,p]=0$ and direct action on a <wavefunction> gives $[U(x),p]=i\hbar U'(x)$,
$$
\boxed{\frac d{dt}\langle p\rangle_\psi
=-\langle U'(x)\rangle_\psi}.
$$
Finally $H$ has no explicit time dependence and $[H,H]=0$, so
$$
\boxed{\frac d{dt}\langle H\rangle_\psi=0}.
$$
The first two equations are the expectation-value counterparts of momentum equals mass times velocity and <Newton's second law>; the last is <conservation of energy>. They become the classical equations directly when the force varies negligibly across the wave packet, so that $\langle U'(x)\rangle\simeq U'(\langle x\rangle)$. These conclusions are summarized by the <classical equations from Ehrenfest theorem>.
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