Regularization of 1/X2 potential in general case of deformed space with minimal length

Abstract

In the general case of deformed Heisenberg algebra leading to the minimal length, we present a definition of the inverse square position operator. Our proposal is based on the functional analysis of the square of the position operator. Using this definition, a particle in the field of the inverse square potential is studied. We obtain analytical and numerical solutions for the energy spectrum of the considerable problem in different cases of deformation function. We conclude that the energy spectrum weakly depends on the choice of deformation function.