Ground State of the Hydrogen Atom via Dirac Equation in a Minimal Length Scenario

TL;DR

This paper investigates how a minimal length, introduced via a deformed Dirac equation, affects the ground state energy of the hydrogen atom, providing a quantum correction in a modified quantum framework.

Contribution

It introduces a minimal length into the Dirac equation using Kempf algebra and calculates the resulting energy shift of the hydrogen atom's ground state.

Findings

Calculated the energy correction due to minimal length effects.

Provided a first-order perturbative estimate of the energy shift.

Demonstrated the impact of quantum gravity-inspired modifications on atomic spectra.

Abstract

In this work we calculate the correction to the ground state energy of the hydrogen atom due to contributions arising from the presence of a minimal length. The minimal length scenario is introduced by means of modifying the Dirac equation through a deformed Heisenberg algebra (kempf algebra). With the introduction of the Coulomb potential in the new Dirac energy operator, we calculate the energy shift of the ground state of the hydrogen atom in first order of the parameter related to the minimal length via perturbation theory.