Effects of Extended Uncertainty Principle on the Relativistic Coulomb Potential

TL;DR

This paper investigates how the extended uncertainty principle influences the relativistic energy spectrum and wavefunctions of Coulomb potential systems in de Sitter and anti-de Sitter spaces, using analytical solutions of Klein-Gordon and Dirac equations.

Contribution

It provides analytical solutions for relativistic Coulomb problems under extended uncertainty principles in curved spacetime backgrounds.

Findings

Modified energy spectra due to extended uncertainty principle

Analytical wavefunctions for Klein-Gordon and Dirac equations

Numerical results for hydrogen-like atom energies

Abstract

The relativistic bound-state energy spectrum and the wavefunctions for the Coulomb potential are studied for de Sitter and anti-de Sitter spaces in the context of the extended uncertainty principle. Klein-Gordon and Dirac equations are solved analytically to obtain the results. The electron energies of hydrogen-like atoms are studied numerically.