The averaged dynamics of the hydrogen atom in crossed electric and magnetic fields as a perturbed Kepler problem

Nils Berglund (1, 2, 3, 4) , Turgay Uzer (1)

1 School of Physics [Atlanta]
2 CPT - Centre de Physique Théorique - UMR 6207
3 D-MATH - Departement Mathematik ETHZ
4 CPT - Centre de Physique Théorique - UMR 7332

We treat the classical dynamics of the hydrogen atom in perpendicular electric and magnetic fields as a celestial mechanics problem. By expressing the Hamiltonian in appropriate action-angle variables, we separate the different time scales of the motion. The method of averaging then allows us to reduce the system to two degrees of freedom, and to classify the most important periodic orbits.

Mots clés: Rydberg atom; crossed fields; Stark effect; Zeeman effect; angle-action variables; Delaunay variables; averaging; Arnol'd diffusion

Domaines: Dynamique Chaotique [nlin.CD]; Physique Atomique [physics.atom-ph]

Nils Berglund, Turgay Uzer. The averaged dynamics of the hydrogen atom in crossed electric and magnetic fields as a perturbed Kepler problem. Foundations of Physics, 2001, 31, pp.283-326. ⟨10.1023/A:1017542620404⟩. ⟨hal-00130545⟩