Ehrenfest's Theorem

From Ladyman & Ross 2007 "Every Thing Must Go" (p. 95: review by Cian Dorr here):

Similarly, the equation (known as Ehrenfest’s theorem), $gradV(⟨r⟩)=m(d^2⟨r⟩/d{t}^2)$, where V is the potential and r is the position operator, exhibits continuity between classical and quantum mechanics.

This formula is not quite correct. The expectation value brackets $⟨.⟩$ are misplaced.

There are many ways of putting it, but in this context, Ehrenfest's Theorem states:

$\frac{d}{dt}⟨p⟩=-⟨\mathrm{\nabla }V⟩$.

This is very similar though to the usual law from classical mechanics, for the rate of change of momentum of a particle in a field $V$:

$\frac{dp}{dt}=-\mathrm{\nabla }V$.