On the nodes of wave function and the quantum Hamilton-Jacobi solution

Abstract

We present the analytic solution for the stationary quantum HamiltonJacobi equation. Knowing the strong relation between the Riccati and quantum Hamilton-Jacobi equations, we develop a simple method to obtain the exact solution. Then, in order to prove the validity of the proposed method, we use two central potentials: the three-dimensional harmonic oscillator and Coulomb potential, both with bound-states. Finally, we compute the action-angle variables in a entirely quantum version for to achieve connect with the nodes of the wave function.