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Closed orbits and their bifurcations in the crossed-fields hydrogen atom

T. Bartsch·J. Main·G. Wunner
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Abstract

A systematic study of closed classical orbits of the hydrogen atom in crossed electric and magnetic fields is presented. We develop a local bifurcation theory for closed orbits which is analogous to the well-known bifurcation theory for periodic orbits and allows identifying the generic closed-orbit bifurcations of codimension one. Several bifurcation scenarios are described in detail. They are shown to have as their constituents the generic codimension-one bifurcations, which combine into a rich variety of complicated scenarios. We propose heuristic criteria for a classification of closed orbits that can serve to systematize the complex set of orbits.

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T. Bartsch, J. Main, G. Wunner. 2002-12-06. Closed orbits and their bifurcations in the crossed-fields hydrogen atom. https://doi.org/10.1103/physreva.67.063410

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