Abstract
A semiclassical analysis, involving asymptotic techniques and the explicit treatment of adiabatic and nonadiabatic behavior, has been developed for potential scattering, resonances and bound state problems in nonrelativistic time independent quantum mechanics. It is here applied to the Hénon-Heiles model, in order to assess the role of regular (normal or local) versus irregular modes in polyatomic molecules.
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References
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The asymptotic nature of this procedure can be proven following, for example, S. F. Feshchenko, N. I. Shkil’, and L. D. Nikolenko, “Asymptotic methods in the theory of linear differential equations”Elsevier, New York (1967).
V.Aquilanti, G.Grossi and F.Pirani, unpublished results, based on the general theory developed in V.Aquilanti and G.Grossi, J.Chem.Phys. 73, 1165 (1980).
See Ref.3 and also V.Aquilanti, G.Grossi and A.Lagana, J.Chem. Phys. 76, 1587 (1982).
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The example discussed here has been limited to states labelled as Qj in Ref.14, but can be extended to QII modes.
B. A. Waite and W. H. Miller, J.Chem.Phys. 74, 3910 (1981); Y. Y. Bay, G. Hose, C. W. McCurdy and H. S. Taylor, to be published.
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© 1985 Plenum Press, New York
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Aquilanti, V., Cavalli, S., Grossi, G. (1985). Semiclassical Analysis of Regular and Irregular Modes of Quantum Coupled Oscillators. In: Casati, G. (eds) Chaotic Behavior in Quantum Systems. NATO ASI Series, vol 120. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2443-0_20
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DOI: https://doi.org/10.1007/978-1-4613-2443-0_20
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