On the integrability of the classical hydrogen atom in a magnetic field
V. M. Pérez-García, J. I. Martín, A. F. Rañada
European Journal of Physics, 13, 160-166 (1992).
MOLAB authors
Abstract
The classical hydrogen atom in a magnetic field is considered as a pedagogical example of the relation between the Hamilton-Jacobi and the Schrodinger equations. When one of them cannot be solved by separation of variables, the same thing can be said of the other. Consequently, as the classical system, not being Liouville integrable, is chaotic, it is not possible to find exact analytic solutions of the Schrodinger equation of the quantum system. The degree of chaos is considered and is related to the lack of conserved quantities. To illustrate the theory the authors present some numerical examples.