Coupled Q-oscillators as a model for vibrations of polyatomic molecules

The system of two $Q$-deformed oscillators coupled so that the total Hamiltonian has the su$_Q$(2) symmetry is proved to be equivalent, to lowest order approximation, to a system of two identical Morse oscillators coupled by the cross-anharmonicity usually used empirically in describing vibrational spectra of triatomic molecules. The symmetry also imposes a connection between the self-anharmonicity of the Morse oscillators and the cross-anharmonicity strength, which can be removed by replacing the $Q$-oscillators by deformed anharmonic oscillators. The generalization to $n$ oscillators is straightforward. The applicability of the formalism to highly symmetric polyatomic molecules is discussed.