I'am having difficulties to understand the so-called classical limit in quantum mechanics. There is a popular method to transform the Schrödinger equation into two coupled equations that are the continuity equation of probability flow and the Hamilton-Jacobi equation with the quantum potential: The Ehrenfest’s theorem and the Quantum Hamilton-Jacobi equation
The limit $\hbar \rightarrow 0$ makes no sense in the Schrödinger picture or in the Heisenberg picture, but somehow it's supposed to make sense in the hydrodynamical picture. Thus, is it obvious that the quantum potential remains finite, as $\hbar \rightarrow 0$, to achieve the statistical version of the classical Hamilton-Jacobi equation?
