Cohen-Tannoudji pp 223
The observable $\mathbf A$ which describes a classically defined physical quantity $\mathscr A$ is obtained by replacing, in the suitably symmetrized expression for $\mathscr A, \mathbf r$ and $\mathbf p$ by the observables $\mathbf R$ and $\mathbf P$ respectively
From above we can say that there exists a velocity operator given as $\displaystyle\mathbf v=\mathbf {\frac{d\hat R}{dt}}$
I've never seen such an expression for velocity operator and I suspect it's wrong. If it's wrong why is it so?