hbar expansions in semiclassical theories for systems with smooth potentials and discrete symmetries

Details hbar expansions in semiclassical theories for systems with smooth potentials and discrete symmetries hbar expansions in semiclassical theories for systems with smooth potentials and discrete symmetries

2005-10-21

arxiv.org/abs/nlin/0510051v2

Annals of Physics 322 (2007), 315-340

Nonlinear Sciences

Chaotic Dynamics

32 pages, 3 figures; accepted for publication in Annals of Physics

Scientific paper

10.1016/j.aop.2006.01.006

We extend a theory of first order hbar corrections to Gutzwiller's trace formula for systems with a smooth potential to systems with discrete symmetries and, as an example, apply the method to the two-dimensional hydrogen atom in a uniform magnetic field. We exploit the C_{4v}-symmetry of the system in the calculation of the correction terms. The numerical results for the semiclassical values will be compared with values extracted from exact quantum mechanical calculations. The comparison shows an excellent agreement and demonstrates the power of the hbar expansion method.

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