3D Quantum Trajectories. Quantum orbits of the Hydrogen's electron

Abstract

In this paper, we introduced the 3D-Quantum Stationary Hamilton Jacobi Equation for a central potential, and established the 3D quantum law of motion of an electron in the presence of such a potential. We established a system of three differential equations from which, and as a numerical application, we plotted the 3D quantum trajectories of the Hydrogen's electron for the ground state and two excited states. we did a comparison between a supposed classical trajectory of the hydrogen electron and the corresponding QTs. We found out that for a particular set of the hidden variables, the QT is close in its shape to the classical one.