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.

Physical Review ADec 1, 199121 citations

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.

Physical Review AJun 1, 199121 citations

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 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.