Exponential-type potentials derived from first principles

Abstract

In this work we study the non-additive quantum mechanics induced by a system with position dependent mass (PDM) from a geometric perspective, using the mathematical formalism of differential geometry. We establish the geometric model from the duality between a particle with PDM that moves in Euclidean space and a particle with constant mass that moves in a curved space. In this approach the deformed momentum characteristic of the non-additive quantum mechanics arises naturally when we determine the symmetries of the metric tensor that describes the curved space. Finally, as an application of this approach we shall study the deformed Coulomb potential and its relation with the Hulthen and Manning–Rosen potentials.