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Semiclassical quantization with bifurcating orbits

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posted on 02.10.2017 by Thomas Bartsch, Jorg Main, Gunter Wunner
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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Physical Review A

Volume

66

Issue

(3)

Pages

033404 (1 - 4)

Citation

BARTSCH, T., MAIN, J. and WUNNER, G., 2002. Semiclassical quantization with bifurcating orbits. Physical Review A, 66(3): 033404.

Publisher

© The American Physical Society

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2002

Notes

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

ISSN

1094-1622

Language

en

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