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

2016/09/05 by L. A. Poveda-Cuevas, F. J. Poveda-Cuevas, Poveda-Cuevas, L. A. +1
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Spectroscopy and Quantum Chemical Studies #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1609.01198

14 pages, 3 figures

arxiv created 2016/09/05 · openalex publication_date 2016/09/05 · arxiv updated 2016/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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