Acta Physica Sinica

q-ROTATING OSCILLATOR MODEL (I)——q-Oscillator and Vibrational Spectra of Diatomic Molecules

YAN HONG, Zhe Chang, Han-Ying Guo, (1)中国高等科学技术中心(世界实验室); (2)中国科学院理论物理研究所,北京,100080

Published Jan 1, 1991• 1 citation

Abstract

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.

DOI: 10.7498/aps.40.1377

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Acta Physica Sinica

q-ROTATING OSCILLATOR MODEL (I)——q-Oscillator and Vibrational Spectra of Diatomic Molecules

YAN HONG, Zhe Chang, Han-Ying Guo, (1)中国高等科学技术中心(世界实验室); (2)中国科学院理论物理研究所,北京,100080

Published Jan 1, 1991• 1 citation

Publisher

Abstract

DOI: 10.7498/aps.40.1377

Related papers

Hq (4) and SUq (2) quantum group symmetries in diatomic molecules

Zhe Chang, Hong Yan

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We develop a model with

{\mathit{H}}_{\mathit{q}}

(4) and

{\mathrm{SU}}_{\mathit{q}}

(2) quantum group symmetries to describe the vibrational and rotational spectra of diatomic molecules. The representations of

{\mathit{H}}_{\mathit{q}}

(4) and

{\mathrm{SU}}_{\mathit{q}}

(2) and solutions to the quantum systems of q oscillators and q rotators are provided. We emphasize that the energy spectra of the q oscillator and q rotator exhibit remarkably the properties of the infrared, vibrational, and rotational Raman spectra as well as vibrational and rotational structures of electronic transitions of the diatomic molecule. When the parameters are properly selected, the spectra of this model coincide with the observed spectra of diatomic molecules. It is suggested that

{\mathit{H}}_{\mathit{q}}

(4) \ensuremath{\bigotimes}

{\mathrm{SU}}_{\mathit{q}}

(2) is an essential symmetry of vibrations and rotations in diatomic molecules.

We suggest the quantum Heisenberg group

{\mathit{H}}_{\mathit{q}(\mathit{J})}

(4) as the dynamical symmetry group of a diatomic-molecule system. The deformation parameter q of the

{\mathit{H}}_{\mathit{q}(\mathit{J})}

(4) symmetry group is a function of J (the quantum number of the angular momentum of the rigid rotation) and characterizes the interaction between vibration and rotation. The vibrational and rotational structures of diatomic molecules are compactly expressed using the quantum-group-theoretic approach. Taylor expansions of the analytic formulas from this approach reproduce the results of the anharmonic-oscillator and the nonrigid-rotator models. For some randomly selected molecules in particular states, the parameters are computed to fit the phenomenological formulas to high accuracy.