Journal of Physics A Mathematical and General

SUq(1,1) description of vibrational molecular spectra

Dennis Bonatsos A, Ernestos N. Argyres, P. P. Raychev

Published Apr 21, 1991• 60 citations

Abstract

The SU q (1,1) quantum algebra is used for the description of vibrational spectra of diatomic molecules for which SU(1,1) is used in the classical approach. While in the classical case only the first two terms of the empirical Dunham expansion occur, in the quantum case all terms are obtained. The improved description of the empirical data is obtained with q being a phase (and not a real number), in agreement with the situation occurring in the q-rotor (having the symmetry SU q (2)) used for the description of rotational spectra of molecules and nuclei.

DOI: 10.1088/0305-4470/24/8/003

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Journal of Physics A Mathematical and General

SUq(1,1) description of vibrational molecular spectra

Dennis Bonatsos A, Ernestos N. Argyres, P. P. Raychev

Published Apr 21, 1991• 60 citations

Publisher

Abstract

DOI: 10.1088/0305-4470/24/8/003

Related papers

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

Zhe Chang, Hong Yan

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 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.

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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.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.

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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.