An Interdisciplinary Journal

2006, Vol.9, No.3, pp.269-275

Semiclassical Quantization of the Diamagnetic Hydrogen Atom at the Field-free Ionization Threshold.
Jörg Main

Semiclassical quantization methods have been successfully applied to the hydrogen atom in a magnetic field at low excitation energies where the classical dynamics is near integrable or weakly chaotic, and at high energies far above the field-free ionization threshold where the classical dynamics is completely hyperbolic. However, the energy region around E=0 has so far resisted any attempts for semiclassical quantization. We present an efficient multi-shooting algorithm for the periodic orbit search and a novel quantization technique based on harmonic inversion with constraints which allow, for the first time, the semiclassical quantization of the diamagnetic hydrogen atom in the very challenging energy region.
Key words: atoms in external fields, nonlinear dynamics, semiclassical quantization

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