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.

Latex, 20 pages, 10 eps figures. figures format changes, included in the body of the paper. redaction changes

References in corpus (5)

• Relativistic Quantum Newton's Law and photon trajectories
• Nodes in the Relativistic Quantum Trajectories and Photon's Trajectories
• The Relativistic Quantum Stationary Hamilton Jacobi Equation for Particle with Spin 1/2
• The 3D Quantum Law of motion
• The Relativistic Quantum Law of motion for a Particle with Spin 1/2