Abstract
An extended concept of the Morse oscillator is presented, where the potential is constructed from several smoothly joined Morse-type (ordinary, reversed or pseudo-Morse) components. The analytic procedures of calculating the complete spectrum of the bound states of the modified Morse oscillator are described. The validity of the asymptotic normalization of the continuum wavefunctions is discussed and a correction method suggested, which takes account of the rigorous sum rules for the complete set of the energy eigenfunctions. All the analytic procedures are illustrated on Xe2 molecule in its 0g+ and 0u+ electronic states.
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