Classical mechanics of the Hydrogen atom perturbed by Van der Waals potential interacting with combined electric and magnetic fields

Abstract

Abstract The hydrogen atom perturbed by Van der Waals potential interacting with combined electric and magnetic fields is a non-integrable system, except for some cases, one of which is separable in elliptical coordinates. A detailed study of the classical mechanics of the system is presented giving a complete description of the real phase space structure of the system, we also determine all the generic bifurcations of Liouville tori. This study is supported by numerical investigations via the Poincare surface of section and the phase space trajectories method. The dynamic character of this system depends on the van der Waals potential and the intensity of the magnetic field. Numerical calculations show that if the separability condition is verified, the classical dynamics is regular. However, with a small change in the condition, the dynamic property of the hydrogen atom begins to change. Since the condition is far from integrable behavior, almost all phase space trajectories are chaotic. On the other hand, the intensity of the electric field has no influence on the system.