Makowski and Konkel [Phys. Rev. A 58, 4975 (1998)] have obtained certain classes of potentials which lead to identical classical and quantum Hamilton-Jacobi equations. We obtain the most general form of these potentials.
We find the form of the potential depending on the coordinates and the time such that a solution, S, of the Hamilton--Jacobi equation yields an exact solution, exp(iS/ℏ), of the corresponding Schrödinger equation.