Noid, D. W. and Marcus, R. A. (1975) Semiclassical calculation of bound states in a multidimensional system. Use of Poincaré's surface of section. Journal of Chemical Physics, 62 (6). pp. 2119-2124. ISSN 0021-9606. http://resolver.caltech.edu/CaltechAUTHORS:NOIjcp75
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A method utilizing integration along invariant curves on Poincaré's surfaces of section is described for semiclassical calculation of eigenvalues. The systems treated are dynamically nonseparable and are quasiperiodic. Use is also made of procedures developed in the previous paper of this series. The calculated eigenvalues for an anharmonically coupled pair of oscillators agree well with the exact quantum values. They also agree with the previous semiclassical calculations in this laboratory, which instead used integrations along the caustics. The present paper increases the number of systems capable of being treated. Using numerical counter examples for nondegenerate systems, it is also shown that an alternative view in the literature, which assumes that periodic trajectories alone suffice, leads to wrong results for the individual eigenvalues.
|Additional Information:||Copyright © 1975 American Institute of Physics. Received 8 November 1974. This research was supported by the Explosives Division, Feltman Research Laboratories, Picatinny Arsenal, Dover, NJ.|
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|Deposited On:||12 Aug 2008 07:14|
|Last Modified:||26 Dec 2012 10:13|
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