Inexistence of the second integral of motion of the classical hydrogen atom in a magnetic field
J. I. Martín, V. M. Pérez-García, A. F. Rañada
Anales de Física A, 87, 48-54 (1991).
MOLAB authors
We study the separation of the center of mass for the hydrogen atom in a homogeneous magnetic field and discuss the range of validity of the usual approximation and its implications on the integrability of the problem. The system turns out to be more chaotic that what is assumed. For fast motion of the center of mass or for strong magnetic field the usual assumption is not valid and the system lacks more than one constant of the motion. This happens in active galactic nuclei or near pulsars.