Journal of Scientific Computing

, Volume 39, Issue 1, pp 1–27

Subharmonic Resonance Behavior for the Classical Hydrogen Atomic System


    • Dept. of Manufacturing EngineeringBoston University
  • Yi Zou
    • One AMD Place

DOI: 10.1007/s10915-008-9248-y

Cite this article as:
Cole, D.C. & Zou, Y. J Sci Comput (2009) 39: 1. doi:10.1007/s10915-008-9248-y


Previously unexplored resonance conditions are shown to exist for the classical hydrogen atomic system, where the electron is treated as a classical charged point particle following the nonrelativistic Lorentz-Dirac equation of motion about a stationary nucleus of opposite charge. For circularly polarized (CP) light directed normal to the orbit, very pronounced subharmonic resonance behavior is shown to occur with a variety of interesting properties. In particular, only if the amplitude of the CP light exceeds a critical value, will the resonance continue without radius and energy decay. A perturbation analysis is carried out to illustrate the main features of the behavior. The present phenomena adds to a growing list of other nonlinear dynamical behaviors of this simple system, that may well be important for more deeply understanding classical and quantum connections.


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© Springer Science+Business Media, LLC 2008