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Physical Review A

Generalized deformed oscillators for vibrational spectra of diatomic molecules

Dennis Bonatsos A, C. Daskaloyannis

Published Jul 1, 1992• 45 citations
Publisher

Abstract

Using deformed bosons, we construct generalized anharmonic oscillators suitable for the description of vibrational spectra of diatomic molecules. One of them gives the same spectrum as the modified P\"oschl-Teller potential, i.e., the first two terms of the Dunham expansion, while the other is a q deformation of the first, corresponding to summing all terms of the Dunham expansion for vibrational molecular spectra.

DOI
10.1103/physreva.46.75

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Using deformed bosons, we construct generalized anharmonic oscillators suitable for the description of vibrational spectra of diatomic molecules. One of them gives the same spectrum as the modified P"oschl-Teller potential, i.e., the first two terms of the Dunham expansion, while the other is a q deformation of the first, corresponding to summing all terms of the Dunham expansion for vibrational molecular spectra.
A generalized deformed oscillator giving the same spectrum as the Morse potential is constructed through the use of quantum-algebraic techniques. The model of n coupled anharmonic oscillators of Iachello and Oss [Phys. Rev. Lett. 66, 2976 (1991)], suitable for the description of vibrational spectra of polyatomic molecules, is subsequently written in terms of such generalized deformed oscillators. In addition to clarifying the relation of the model of Iachello and Oss to other models using coupled oscillators for the description of vibrational molecular spectra, the present formalism allows for the construction of a large class of exactly soluble models with no extra computational effort. As an example, the way of including a coupling of the Darling-Dennison type is shown.
A generalized deformed oscillator, with eigenvalues equal to the eigenvalues of the Schrodinger equation with the modified Poschl-Teller potential, is constructed. For special values of the potential depth the deformed oscillator algebra has a finite-dimensional irreducible representation. The polynomial representation and the associate deformed operations of integration and differentiation are studied. The results of this study are general and they can be applied directly to the case of the q-deformed oscillator, with q being a root of unity.
We suggest a model of q-deformed rotating oscillator which possesses the symmetry of quantum group and point out that this model can be used to describe the vibrational and rotational structures of many microscopic systems. We construct the representation of q-oscilla or algebra and give energy values of q-oscillaor in this representation. It is shown that the q-oscillator spectra can be used to describe infrared spectra, Raman spectra and vibrational structure of electronic transitions of diatomic molecules.
In this paper, we consider the one-dimensional anharmonic oscillator, which represents well the anharmonic vibrations in diatomic molecules. For the description of the associate potential we use the Morse potential, which gives a good approximation of the experimentally observed vibrational modes of molecules and hence contributes to the realistic description of the spectrum of diatomic molecules. The generalized and Gaussian coherent states are thus constructed and compared in terms of the localization of the particle in those states. We apply these results to the example of the sodium chloride molecule, 1 H 35 Cl.
q-deformation of the U(1) dynamical symmetry of U(2) group is introduced for the first time for vibrations of diatomic molecules. The question of pure real and pure imaginary value of q-deformation parameter, often raised in the literature, is found to be related to the particular choice of the constants of the model. The complex q-deformation parameter is allowed, with pure real and pure imaginary values as its special cases. Compared to the other dynamical symmetry Oq(2) of Uq(2), the result of Uq(1) of Uq(2) remains better even when the vibron number in Oq(2) is varied. The role of the vibron number in the two dynamical symmetries of U(2) is shown to be different. In Uq(1) symmetry, the vibron number is fixed by the number of observed states of the system since Uq(1) represents the q-deformation of a truncated anharmonic oscillator. A possible physical meaning to the q-deformation parameter is suggested in terms of higher order anharmonicities of the truncated anharmonic oscillator.