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C 1 non-integrability of a hydrogen atom in a circularly polarized microwave field

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Central European Journal of Physics

Abstract

Barrabés et al. [Physica D, 241(4), 333–349, 2012] consider the problem of the hydrogen atom interacting with a circularly polarized microwave field modeled as a planar perturbed Kepler problem. For different values of the parameter, the authors offer some numerical evidence of the non-integrability of this problem. The objective of the present work is to give an analytical proof of the C1 non-integrability of this problem for any value of the parameter using the averaging theory as a main tool.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada y Estadística Universidad Politécnica de Cartagena, Hospital de Marina, 30203, Cartagena, Región de Murcia, Spain

    Juan L. G. Guirao

  2. Departamento de Matemáticas, Universidad de Castilla-La Mancha, E.U. Politécnica de Cuenca, Campus Universitario, 16071, Cuenca, Castilla La-Mancha, Spain

    Miguel A. López

  3. Centro Universitario de la Defensa, Academia General del Aire, Universidad Politécnica de Cartagena, 30720, Santiago de la Ribera, Región de Murcia, Spain

    Juan A. Vera

Authors
  1. Juan L. G. Guirao
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  2. Miguel A. López
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  3. Juan A. Vera
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Corresponding author

Correspondence to Juan L. G. Guirao.

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Guirao, J.L.G., López, M.A. & Vera, J.A. C 1 non-integrability of a hydrogen atom in a circularly polarized microwave field. centr.eur.j.phys. 10, 742–748 (2012). https://doi.org/10.2478/s11534-012-0077-0

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  • DOI: https://doi.org/10.2478/s11534-012-0077-0

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