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arXiv:hep-th/9511084 · Journal of Physics A Mathematical and General

Multidimensional isotropic and anisotropicq-oscillator models

A Ghosh, P Mitra, A Kundu

Published Jan 7, 1996• 3 citations
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Abstract

q-oscillator models are considered in two and higher dimensions and their symmetries are explored. New symmetries are found for both isotropic and anisotropic cases. Applications to the spectra of triatomic molecules and superdeformed nuclei are discussed.
DOI
10.1088/0305-4470/29/1/013

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The system of two QQQ-deformed oscillators coupled so that the total Hamiltonian has the suQ_QQ​(2) symmetry is proved to be equivalent, to lowest order approximation, to a system of two identical Morse oscillators coupled by the cross-anharmonicity usually used empirically in describing vibrational spectra of triatomic molecules. The symmetry also imposes a connection between the self-anharmonicity of the Morse oscillators and the cross-anharmonicity strength, which can be removed by replacing the QQQ-oscillators by deformed anharmonic oscillators. The generalization to nnn oscillators is straightforward. The applicability of the formalism to highly symmetric polyatomic molecules is discussed.
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Abstract In both classical and quantum physics the harmonic oscillator is one of the most important physical systems [1–4]. Furthermore, because of the simplicity and symmetry of the Hamiltonian operator, the quantum mechanical oscillator is particularly suited to analysis by abstract operator methods. For this reason the study of the one dimensional oscillator is a useful introduction to the application of operator methods in quantum mechanics. In Sections 2.1–2.4 we use these methods to determine energy eigenvalues and eigenkets, and matrix elements; the analysis is extended to isotropic multidimensional oscillators in Section 2.10. Quasiclassical states of the oscillator are discussed in Section 2.5. In Section 2.6 shift operators are used to calculate wave functions. In Sections 2.7–2.11 we discuss some applications of the theory of the oscillator.