Regularity and Chaos in the Hydrogen Atom Highly Excited with a Strong Magnetic Field

M Amdouni,H Eleuch

doi:10.1155/2014/957652

Abstract

The effects of the relativistic corrections on the energy spectra are analyzed. Effective simulations based on manipulations of operators in the Sturmian basis are developed. Discrete and continuous energy spectra of a hydrogen atom with realistic nucleus mass in a strong magnetic field are computed. The transition from regularity to chaos in diamagnetic problem with the effect of the nucleus recoil energy is explored. Anticrossing of energy levels is observed for strong magnetic field.

Highlights

A lot of works have been recently dedicated to the study of two- or multilevel systems such as Rydberg atom, excitonic systems, and nanoresonators [1,2,3,4,5,6,7,8,9,10,11,12,13]
Its great importance lies in its implication in different branches of physics: astrophysics [9, 12], atomic physics [14,15,16,17], molecular physics [18, 19], spectroscopy [20, 21], solid state [22], and plasma physics [23]
The Rydberg atom in a static magnetic field is a simple system which can be investigated experimentally and theoretically. It turns out a prototype of quantum systems whose classical behavior may show chaotical dynamics [38,39,40,41,42]

Summary

Introduction

A lot of works have been recently dedicated to the study of two- or multilevel systems such as Rydberg atom, excitonic systems, and nanoresonators [1,2,3,4,5,6,7,8,9,10,11,12,13]. Its great importance lies in its implication in different branches of physics: astrophysics [9, 12], atomic physics [14,15,16,17], molecular physics [18, 19], spectroscopy [20, 21], solid state [22], and plasma physics [23] It leads to interesting quantum features such as soliton propagation [24,25,26,27,28,29,30], entanglement [31, 32], antibunching [33], squeezing [34], bistability [35], and chaos [36, 37]. The Rydberg atom in a static magnetic field is a simple system which can be investigated experimentally and theoretically It turns out a prototype of quantum systems whose classical behavior may show chaotical dynamics [38,39,40,41,42]. These constants of motion allow remaining unchanged, for instance, the regularly spaced energy levels [38]

Objectives

Methods

Conclusion