BARTSCH, T., MAIN, J. and WUNNER, G., 2002. Semiclassical quantization with bifurcating orbits. Physical Review A, 66(3): 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.
This paper was accepted for publication in the journal Physical Review A and the definitive published version is available at https://doi.org/10.1103/PhysRevA.66.033404