Semiclassical quantization with bifurcating orbits
Chaotic Dynamics
2009-11-07 v1
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.
Cite
@article{arxiv.nlin/0203033,
title = {Semiclassical quantization with bifurcating orbits},
author = {T. Bartsch and J. Main and G. Wunner},
journal= {arXiv preprint arXiv:nlin/0203033},
year = {2009}
}