On Some Quantum Correction to the Coulomb Potential in Generalized Uncertainty Principle Approach

TL;DR

This paper investigates quantum corrections to the Coulomb potential derived from a generalized uncertainty principle, proposing a Bethe ansatz method to solve the modified Schrödinger equation and exploring implications for quantum gravity and information.

Contribution

It introduces a novel approach to solving a modified Schrödinger equation with quantum gravity corrections using Bethe ansatz, addressing the minimal length scale effects.

Findings

Quantum mechanically corrected gravitational interaction proposed.

Bethe ansatz successfully applied to the modified equation.

Insights into quantum gravity implications from the correction.

Abstract

Taking into account the importance of the unified theory of quantum mechanics and gravity, and the existence of a minimal length of the order of the Planck scale, we consider a modified Schr\"odinger equation resulting from a generalized uncertainty principle, which finds applications from the realm of quantum information to large-scale physics, with a quantum mechanically corrected gravitational interaction proposed very recently. As the resulting equation cannot be solved by common exact approaches, we propose a Bethe ansatz approach, which will be applied and whose results we will discuss, commenting on the analogy of the present study with some other interesting physical problems.