  In a stationary case and for any potential, we solve the three-dimensional
quantum Hamilton-Jacobi equation in terms of the solutions of the corresponding
Schrodinger equation. Then, in the case of separated variables, by requiring
that the conjugate momentum be invariant under any linear transformation of the
solutions of the Schrodinger equation used in the reduced action, we clearly
identify the integration constants successively in one, two and three
dimensions. In each of these cases, we analytically establish that the quantum
Hamilton-Jacobi equation describes microstates not detected by the Schrodinger
equation in the real wave function case.
