On the relation between the Kratzer molecular potential and a set of displaced morse oscillator potentials

Abstract

AbstractThe radial Schrödinger equation for the Kratzer molecular potential is equivalent to that of a radial Coulomb problem with an effective (nonintegral) value of rotational angular momentum. The radial Coulomb and the Morse oscillator problems provide different realizations of the algebra so(2,1), whereby the Casimir operators of the Coulomb and Morse oscillator problems are related to the angular momentum quantum number and to the energy, respectively. These relationships permit mappings between the Kratzer molecular potential and the Morse oscillator potential 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 oscillators. The ground vibrational level of the Kratzer potential is mapped onto the ground vibrational level of a specific Morse oscillator and the remaining (infinite) set of higher vibrational levels are mapped onto 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 contrasted with that of the finite set of displaced Morse potentials arising as supersymmetric partner potentials to a given parent Morse potential, where there is a systematic unit decrease in the number of bound vibrational levels and a successive increase in equilibrium separation. © 1994 John Wiley & Sons, Inc.