DOI: 10.1063/1.447487. Quantization with operators appropriate to shapes of trajectories and classical perturbation theory

Quantization with operators appropriate to shapes of trajectories and classical perturbation theory

10.1063/1.447487

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

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 Weyl 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.

Bibliography

Uzer, T., & Marcus, R. A. (1984). Quantization with operators appropriate to shapes of trajectories and classical perturbation theory. The Journal of Chemical Physics, 81(11), 5013â5023.

Authors 2

T. Uzer (first)
R. A. Marcus (additional)

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Dates

Type	When
Created	22 years, 6 months ago (Feb. 28, 2003, 12:34 p.m.)
Deposited	1 year, 6 months ago (Feb. 9, 2024, 9:46 p.m.)
Indexed	1 year, 6 months ago (Feb. 11, 2024, 7:59 a.m.)
Issued	40 years, 9 months ago (Dec. 1, 1984)
Published	40 years, 9 months ago (Dec. 1, 1984)
Published Print	40 years, 9 months ago (Dec. 1, 1984)

Funders 0

None

BibTeX

@article{Uzer_1984, title={Quantization with operators appropriate to shapes of trajectories and classical perturbation theory}, volume={81}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.447487}, DOI={10.1063/1.447487}, number={11}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Uzer, T. and Marcus, R. A.}, year={1984}, month=dec, pages={5013–5023} }

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