The hydrogen atom in an electric field: Closed-orbit theory with bifurcating orbits
Abstract
Closed-orbit theory provides a general approach to the semiclassical description of photo-absorption spectra of arbitrary atoms in external fields, the simplest of which is the hydrogen atom in an electric field. Yet, despite its apparent simplicity, a semiclassical quantization of this system by means of closed-orbit theory has not been achieved so far. It is the aim of this paper to close that gap. We first present a detailed analytic study of the closed classical orbits and their bifurcations. We then derive a simple form of the uniform semiclassical approximation for the bifurcations that is suitable for an inclusion into a closed-orbit summation. By means of a generalized version of the semiclassical quantization by harmonic inversion, we succeed in calculating high-quality semiclassical spectra for the hydrogen atom in an electric field.
Keywords
Cite
@article{arxiv.nlin/0212046,
title = {The hydrogen atom in an electric field: Closed-orbit theory with bifurcating orbits},
author = {T. Bartsch and J. Main and G. Wunner},
journal= {arXiv preprint arXiv:nlin/0212046},
year = {2009}
}