U-Q(2)SUPERSET-OF-U-Q(1) DESCRIPTION OF VIBRATIONAL-SPECTRA OF DIATOMIC-MOLECULES

q-deformation of the U(1) dynamical symmetry of U(2) group is introduc ed for the first time for vibrations of diatomic molecules. The questi on of pure real and pure imaginary value of q-deformation parameter, o ften raised in the literature, is found to be related to the particula r choice of the constants of the model. The complex q-deformation para meter is allowed, with pure real and pure imaginary values as its spec ial cases. Compared to the other dynamical symmetry O-q(2) Of U-q(2), the result of U-q(1) Of U-q(2) remains better even when the vibron num ber in O-q(2) is varied. The role of the vibron number in the two dyna mical symmetries of U(2) is shown to be different. In U-q(1) symmetry, the vibron number is fixed by the number of observed states of the sy stem since U-q(1) represents the q-deformation of a truncated anharmon ic oscillator. A possible physical meaning to the q-deformation parame ter is suggested in terms of higher order anharmonicities of the trunc ated anharmonic oscillator.