Mie-type potential from a class of multiparameter exponential-type potential: Bound state solutions in D dimensions

The Mie potential is a model of molecular interaction, very useful in the study of diatomic molecules because allows one to describe the softness/hardness of the repulsive interactions as well as the range of attraction. As a consequence, the Mie potential and one of their particular cases, the Lennard-Jones potential, have been extensively used in many branches of physics and chemistry. In this work, the exact bound state solutions of the D-dimensional Schrödinger equation with the Mie-type potential are presented. These eigen-functions/values are obtained as a particular case of the exactly solvable Schrödinger equation for a class of multiparameter exponential-type potential. Furthermore our approach does not need any approximation to the centrifugal term. As an example of the usefulness of our proposition, we show how the bound state solutions of the Kratzer-Fues and Coulomb potentials in D-dimensions are particular cases from the proposal.