Semiclassical quantization with bifurcating orbits

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.

References in corpus (2)

• Use of Harmonic Inversion Techniques in Semiclassical Quantization and Analysis of Quantum Spectra
• Decimation and Harmonic Inversion of Periodic Orbit Signals

Cited by in corpus (3)

• Semiclassical quantization of the hydrogen atom in crossed electric and magnetic fields
• Photoabsorption spectra of the diamagnetic hydrogen atom in the transition regime to chaos: Closed orbit theory with bifurcating orbits
• Uniform semiclassical approximations on a topologically non-trivial configuration space: The hydrogen atom in an electric field