Eur. Phys. J. D 27, 3-13 (2003)
https://doi.org/10.1140/epjd/e2003-00233-3

Rydberg hydrogen atom in the presence of uniform magnetic and quadrupolar electric fields

A quantum mechanical, classical and semiclassical approach

Area de Física Aplicada, Universidad de La Rioja, Logroño, Spain

Corresponding author: ^a josepablo.salas@dq.unirioja.es

Received: 17 March 2003
Revised: 6 May 2003
Published online: 29 July 2003

Abstract

We present a quantum mechanical, classical and semiclassical study of the energy spectrum of a Rydberg hydrogen atom in the presence of uniform magnetic and quadrupolar electric fields. Here we study the case that the z-component of the canonical angular momentum is zero. In this sense, the dynamics depends on a dimensionless parameter λ representing the relative strengths of both fields. We consider that both external fields act like perturbations to the pure Coulombian system. In the classical study we find that, depending on the λ value, the phase flow shows four different regimes made up of vibrational and rotational trajectories, which are connected, respectively with the degenerate energy levels of double symmetry, and with the non-degenerate energy levels. The transit from one regime to another takes place by means of three oyster bifurcations. The semiclassical results are in good agreement with the results of the quantum mechanical calculations within the first-order perturbation theory. Moreover, we find that the evolution of the quantum/semiclassical energy spectrum can be explained by means of a classical description.