Q-DEFORMED MORSE OSCILLATOR

Using the exact realization of the Morse oscillator problem in terms of SO(2,1) symmetry and its bosonization, the corresponding q deformation is performed. The ground-state energy is found to remain constant for all arbitrary (zero, real, imaginary, or complex) values of the q-deformation parameter. By fitting the resulting q-deformed energy-level spectrum to data for the hydrogen molecule in its ground electronic state, it is shown that, depending upon the value of the scaling constant, a considerable improvement results for the real and/or imaginary q deformation over the corresponding result for the classical Morse oscillator, and that the best fit is obtained in the q-deformed case with a complex value of the deformation parameter.