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85035217131
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A. Voros, J. Zinn-Justin, M.-J. Giannoni, North-Holland, Amsterdam
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O. Bohigas, in Chaos and Quantum Physics, Proceedings of the Les Houches Summer School, Session LII, edited by A. Voros, and J. Zinn-Justin, M.-J. Giannoni (North-Holland, Amsterdam, 1990), p. 87.
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Chaos and Quantum Physics, Proceedings of the Les Houches Summer School, Session LII
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Bohigas, O.1
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17
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0001035040
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Phys. Rev. E
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Eckhardt, B.1
Fishman, S.2
Keating, J.3
Agam, O.4
Main, J.5
Müller, K.6
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27
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36149035308
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A. Hayli, Th. Dumont, J. Moulin-Ollagnier, and J.-M. Strelcyn, J. Phys. A 20, 3237 (1987).
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Hayli, A.1
Dumont, T.2
Moulin-Ollagnier, J.3
Strelcyn, J.-M.4
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31
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85037192347
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Due to the (Formula presented) symmetry of Eq. (3), the stable orbit perpendicular to the field is already periodic after half of its full period; consequently, (Formula presented) takes only even values. States with positive (negative) z parity (Formula presented) symmetry with respect to (Formula presented) have even (odd) quantum numbers (Formula presented)
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Due to the (Formula presented) symmetry of Eq. (3), the stable orbit perpendicular to the field is already periodic after half of its full period; consequently, (Formula presented) takes only even values. States with positive (negative) z parity (Formula presented) symmetry with respect to (Formula presented) have even (odd) quantum numbers (Formula presented).
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32
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85037208440
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The assignment of quantum numbers may be checked by comparison with the corresponding Gutzwiller eigenvalues (Formula presented) cf. 27
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The assignment of quantum numbers may be checked by comparison with the corresponding Gutzwiller eigenvalues (Formula presented) cf. 27.
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33
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85037194890
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the case of the hydrogen atom, (Formula presented) is not simply proportional to (Formula presented) It can be shown that in the present case periods are to be replaced by scaled actions in semiclassical expressions. Hence, we require trajectory segments satisfying (Formula presented). It is still possible to use semiclassical sum rules by appealing to the fact that on average, (Formula presented) are proportional to (Formula presented)
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In the case of the hydrogen atom, (Formula presented) is not simply proportional to (Formula presented) It can be shown that in the present case periods are to be replaced by scaled actions in semiclassical expressions. Hence, we require trajectory segments satisfying (Formula presented). It is still possible to use semiclassical sum rules by appealing to the fact that on average, (Formula presented) are proportional to (Formula presented)
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