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.

Physical Review AJun 1, 199121 citations

Quantum Group Symmetry of the Hubbard Model

E. Ahmed, A. S. Hegazi

International Journal of Theoretical PhysicsSep 1, 20000 citations

SUq(1,1) description of vibrational molecular spectra

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

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.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.

Journal of Physics A Mathematical and GeneralApr 21, 199160 citations

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.