Semiclassical quantization with bifurcating orbits

Details Semiclassical quantization with bifurcating orbits Semiclassical quantization with bifurcating orbits

2002-03-15

arxiv.org/abs/nlin/0203033v1

Phys. Rev. A 66, 033404 (2002)

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1103/PhysRevA.66.033404

Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra involving uniform approximations. As a prototype example, the method is shown to yield excellent results for photo-absorption spectra for the hydrogen atom in an electric field in a spectral range where the abundance of bifurcations would render the standard closed-orbit formula without uniform approximations useless. Our method immediately applies to semiclassical trace formulae as well as closed-orbit theory and offers a general technique for the semiclassical quantization of arbitrary systems.

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