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arXiv · 1609.01198

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

L. A. Poveda-Cuevas·F. J. Poveda-Cuevas
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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.

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L. A. Poveda-Cuevas, F. J. Poveda-Cuevas. 2016-09-05. On the nodes of wave function and the quantum Hamilton-Jacobi solution. https://arxiv.org/abs/1609.01198

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