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Semiclassical quantization with bifurcating orbits

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journal contribution
posted on 02.10.2017, 10:33 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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