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 photoabsorption 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 formulas as well as the closed-orbit theory and offers a general technique for the semiclassical quantization of arbitrary systems.
- Received 15 March 2002
DOI:https://doi.org/10.1103/PhysRevA.66.033404
©2002 American Physical Society