One-dimensional Coulomb-like problem in general case of deformed space with minimal length

TL;DR

This paper derives exact solutions for a 1D Coulomb-like problem in a deformed space with minimal length, analyzing how different deformations affect the energy spectrum and eigenfunctions.

Contribution

It provides a general definition of the inverse position operator in deformed Heisenberg algebra and solves the Coulomb-like problem exactly in this context.

Findings

Energy spectrum depends strongly on the deformation function

Exact eigenfunctions are obtained in momentum space

Deformation corrections vary with different deformation functions

Abstract

We present a definition of the two-sided inverse of position operator in general case of deformed Heisenberg algebra leading to minimal length. Energy spectrum and eigenfunctions in momentum space for 1D Coulomb-like potential in deformed space are found exactly. We analyse the energy spectrum for different partial cases of deformation function and find that correction due to the deformation highly depends on type of the deformation function.