# Regularization of $1/X^2$ potential in general case of deformed space with minimal length

## TL;DR

This paper defines the inverse square position operator within a deformed Heisenberg algebra framework with minimal length and analyzes the energy spectrum of a particle in this potential, revealing slight dependence on deformation functions.

## Contribution

It introduces a new definition of the inverse square position operator in deformed space and studies its spectral properties.

## Key findings

- Energy spectrum slightly depends on deformation function
- Analytical and numerical solutions obtained
- Potentially relevant for quantum gravity models

## Abstract

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