ISSN:
1432-2234
Keywords:
Hénon-Heiles potential
;
Coupled oscillators
;
Adiabatic representation
;
Chaotic quantum modes
;
Elliptic umbilic catastrophes
;
Resonance widths
Source:
Springer Online Journal Archives 1860-2000
Topics:
Chemistry and Pharmacology
Notes:
Abstract The quantum mechanics of the Hénon-Heiles potential is analyzed using an adiabatic representation in polar coordinates and exploiting the asymptotic separability of the radius. The procedure allows us to establish a correlation between quasiperiodic and chaotic classical behavior, and regular or irregular quantum modes: It is found that irregularity can be attributed to nonadiabatic effects at the potential ridge. The resonance widths for this prototypic system of coupled oscillators are studied with reference to the lifetime in the quantum theory of unimolecular decay. The near separability of the radius of the polar coordinate representation is exploited for discussing energy dependence and symmetry effects on the widths. The relevance of this analysis for the characterization of quantum mechanical behavior near an elliptic umbilic catastrophe point is also briefly considered.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01151231
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