Conclusions
In summary, we have shown that the Hamiltonian of an electron in combined Coulomb and crossed external electric and magnetic fields can be usefully approximated by combining Normal Form theory and Lie algebra. Despite the enormous size of the parameter and phase space of the original problem, the special status assigned to some intricate periodic motions of the electron by recent experiments is connected to adiabatic invariants through our treatment. While deviations from the Coulomb potential require slight changes in our arguments due to finite core size, the success of the adiabatic invariants in explaining key features of the experiment shows their potential value for simplifying other aspects of this complex problem in the future.
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von Milczewski, J., Uzer, T. (2002). Adiabatic Invariants of Rydberg Electrons in Crossed Fields. In: Schmelcher, P., Schweizer, W. (eds) Atoms and Molecules in Strong External Fields. Springer, Boston, MA. https://doi.org/10.1007/0-306-47074-8_25
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DOI: https://doi.org/10.1007/0-306-47074-8_25
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