On the nodes of wave function and the quantum Hamilton-Jacobi solution
Mathematical Physics
2016-09-06 v1 math.MP
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.
Keywords
Cite
@article{arxiv.1609.01198,
title = {On the nodes of wave function and the quantum Hamilton-Jacobi solution},
author = {L. A. Poveda-Cuevas and F. J. Poveda-Cuevas},
journal= {arXiv preprint arXiv:1609.01198},
year = {2016}
}
Comments
14 pages, 3 figures