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Semiclassical calculation of eigenvalues for higher order resonances in nonseparable oscillator systems

Noid, D. W. and Marcus, R. A. (1986) Semiclassical calculation of eigenvalues for higher order resonances in nonseparable oscillator systems. Journal of Chemical Physics, 85 (6). pp. 3305-3312. ISSN 0021-9606. http://resolver.caltech.edu/CaltechAUTHORS:NOIjcp86

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Abstract

It is shown how the "trajectory-close method" introduced in earlier papers of this series can be used to treat other resonant systems semiclassically. The method, which does not involve the use of any curvilinear coordinate system, is illustrated for two coupled oscillators which have 3:1, 4:1, 5:1, 3:2, and 5:2 internal resonances. It is readily executed and it is shown how it can be extended to the three-oscillator case. This work supplements our earlier studies of 1:1, 2:1, and 3:1 resonant systems using this technique. Shapes of eigentrajectories and of corresponding quantum mechanical wave functions are compared for each of these systems. The paper also contains a survey of and comparison with other semiclassical methods which have been applied to systems with internal resonances


Item Type:Article
Additional Information:Copyright © 1986 American Institute of Physics. Received 26 August 1985; accepted 28 May 1986. We are pleased to acknowledge the support of this research by the U.S. Department of Energy and by a grant from the National Science Foundation. Research supported by the U.S. Department of Energy under contract DE-AC05-84OR21400 with Martin Marietta Energy Systems, Inc. Noyes Laboratory of Chemical Physics, Contribution No. 7269.
Subject Keywords:SEMICLASSICAL APPROXIMATION, QUANTUM MECHANICS, EIGENVALUES, RESONANCE, COORDINATES
Record Number:CaltechAUTHORS:NOIjcp86
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:NOIjcp86
Alternative URL:http://dx.doi.org/10.1063/1.450951
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10941
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:20 Jun 2008
Last Modified:26 Dec 2012 10:06

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