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

Analytical Solutions of the Quantum Hamilton-Jacobi Equation and Exact WKB-Like Representations of One-Dimensional Wave Functions