ON THE RELATION BETWEEN THE KRATZER MOLECULAR-POTENTIAL AND A SET OF DISPLACED MORSE OSCILLATOR POTENTIALS

The radial Schrodinger equation for the Kratzer molecular potential is equivalent to that of a radial Coulomb problem with an effective (non integral) value of rotational angular momentum. The radial Coulomb and the Morse oscillator problems provide different realizations of the a lgebra so(2, 1), whereby the Casimir operators of the Coulomb and Mors e oscillator problems are related to the angular momentum quantum numb er and to the energy, respectively. These relationships permit mapping s between the Kratzer molecular potential and the Morse oscillator pot ential such that the vibrational energy levels of a Kratzer potential with a fixed rotational angular momentum quantum number may be mapped onto degenerate vibrational levels of a set of displaced Morse oscilla tors. The ground vibrational level of the Kratzer potential is mapped onto the ground vibrational level of a specific Morse oscillator and t he remaining (infinite) set of higher vibrational levels are mapped on to degenerate states of displaced Morse oscillators, corresponding to systematic unit increase in the number of bound vibrational levels and successive decrease in equilibrium separation. This behavior is contr asted with that of the finite set of displaced Morse potentials arisin g as supersymmetric partner potentials to a given parent Morse potenti al, where there is a systematic unit decrease in the number of bound v ibrational levels and a successive increase in equilibrium separation. (C) 1994 John Wiley & Sons, Inc.