Solving the Kratzer oscillator in diatomic molecules: an algebraic approach based on the so(2,1) Lie algebra

Abstract

In this article, we solve the rovibrational Schrodinger equation for diatomic molecules using the Kratzer oscillator bymeans of the so(2, 1) Lie algebra. Themain contribution of our algebraic approach is that this allows us to reduce the degree of the Schrodinger equation giving thus a first-order differential equation, by which the vibrational ground state wave function is obtained, clearly and in few steps. The energies are obtained by scaling of the observables r and p(r) which preserves the canonical commutation relation, and a recurrence relation for the bound states written in terms of the raising operator is also given. Also we calculate the rovibrational spectrum of H-2 and CO molecules, showing that the energies of the Kratzer oscillator not only depends on vibrational and rotational quantum numbers, but also in the difference between the vibrational quantum number with its minimum value, for a fixed l. The article ends giving a physical insight of the symmetry transformation of the SO(2, 1) Lie group in order to show the relationship between this group and its associated Lie algebra. Finally, as an illustrative example, we calculated the selection rules for the vibrational quantum number, from a purely algebraic approach.