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Semiclassical quantization with bifurcating orbits

T. Bartsch·J. Main·G. Wunner
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Abstract

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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BibTeXRIS

T. Bartsch, J. Main, G. Wunner. 2002-03-15. Semiclassical quantization with bifurcating orbits. https://doi.org/10.1103/physreva.66.033404

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