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

Abstract

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.