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
energy region.
Key words:
atoms in external fields, nonlinear dynamics, semiclassical
quantization
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