Uzer, T. and Marcus, R. A. (1984) Quantization with operators appropriate to shapes of trajectories and classical perturbation theory. Journal of Chemical Physics, 81 (11). pp. 5013-5023. ISSN 0021-9606. http://resolver.caltech.edu/CaltechAUTHORS:20120703-092820677
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Quantization is discussed for molecular systems having a zeroth order pair of doubly degenerate normal modes. Algebraic quantization is employed using quantum operators appropriate to the shape of the classical trajectories or wave functions, together with Birkhoff-Gustavson perturbation theory and the W eyl correspondence for operators. The results are compared with a previous algebraic quantization made with operators not appropriate to the trajectory shape. Analogous results are given for a uniform semiclassical quantization based on Mathieu functions of fractional order. The relative sensitivities of these two methods (AQ and US) to the use of operators and coordinates related to and not related to the trajectory shape is discussed. The arguments are illustrated using principally a Hamiltonian for which many previous results are available.
|Additional Information:||© 1984 American Institute of Physics. Received 5 July 1984; accepted 18 July 1984. We are pleased to acknowledge the support of this research by the National Science Foundation.|
|Subject Keywords:||perturbation theory; wave functions; hamiltonian function; vibrational states; semiclassical approximation; quantum mechanics|
|Other Numbering System:|
|Classification Code:||PACS: 03.65.Sq; 31.15.-p|
|Official Citation:||Quantization with operators appropriate to shapes of trajectories and classical perturbation theory T. Uzer and R. A. Marcus, J. Chem. Phys. 81, 5013 (1984), DOI:10.1063/1.447487|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Aucoeur Ngo|
|Deposited On:||03 Jul 2012 16:56|
|Last Modified:||26 Dec 2012 15:27|
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