2006, Vol.9, No.3, pp.269-275
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
Key words: atoms in external fields, nonlinear dynamics, semiclassical quantization
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