  General analytical solutions of the Quantum Hamilton Jacobi Equation for
conservative one-dimensional or reducible motion are presented and discussed.
The quantum Hamilton's characteristic function and its derivative, i.e. the
quantum momentum function, are obtained in general, and it is shown that any
one-dimensional wave function can be exactly represented in a WKB-like form.
The formalism is applied to the harmonic oscillator and to the electron's
motion in the hydrogen atom, and the above mentioned functions are computed and
discussed for different quantum numbers. It is analyzed how the quantum
quantities investigated tend to the corresponding classical ones, in the limit
$\hbar\to 0$. These results demonstrate that the Quantum Hamilton Jacobi
Equation is not only completely equivalent to the Schr\"odinger Equation, but
allows also to fully investigate the transition from quantum to classical
mechanics.
