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Semiclassical quantization of the hydrogen atom in crossed electric and magnetic fields

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journal contribution
posted on 21.05.2019, 13:25 by Thomas Bartsch, Jorg Main, Gunter Wunner
The S-matrix theory formulation of closed-orbit theory recently proposed by Granger and Greene is extended to atoms in crossed electric and magnetic fields. We present a semiclassical quantization of the hydrogen atom in crossed fields, which succeeds in resolving individual lines in the spectrum, but is restricted to the strongest lines of each n manifold. By means of a detailed semiclassical analysis of the quantum spectrum, we demonstrate that it is the abundance of bifurcations of closed orbits that precludes the resolution of finer details. They necessitate the inclusion of uniform semiclassical approximations into the quantization process. Uniform approximations for the generic types of closed-orbit bifurcations are derived, and a general method for including them in a high-resolution semiclassical quantization is devised.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Phys. Rev. A

Volume

67

Pages

. 063411 - ?

Citation

BARTSCH, T., MAIN, J. and WUNNER, G., 2003. Semiclassical quantization of the hydrogen atom in crossed electric and magnetic fields. Physical Review A , 67: 063411.

Publisher

© The American Physical Society

Version

VoR (Version of Record)

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

2003

Notes

This paper was accepted for publication in the journal Physical Review A, and the definitive published version is available at http://doi.org/10.1103/PhysRevA.67.063411

ISSN

1050-2947

eISSN

1094-1622

Language

en

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