Spherically symmetric potential in noncommutative spacetime with a compactified extra dimensions

TL;DR

This paper investigates the energy spectra of quantum models like the hydrogen atom in noncommutative spacetime with compactified extra dimensions, providing analytical solutions in higher-dimensional settings.

Contribution

It offers the first analytical spectrum calculations for hydrogen-like models in 4+1 dimensional noncommutative spacetime with compactified dimensions.

Findings

Analytical spectrum for hydrogen atom in 4+1 dimensions derived.

Extension to Yukawa potential in noncommutative spacetime.

Discussion of higher-dimensional cases D ≥ 4.

Abstract

The Schr\"odinger equation of the spherical symmetry quantum models such as the hydrogen atom problem seems to be analytically non-solvable in higher dimensions. When we try to compactifying one or several dimensions this question can maybe solved. This paper stands for the study of the spherical symmetry quantum models on noncommutative spacetime with compactified extra dimensions. We provide analytically the resulting spectrum of the hydrogen atom and Yukawa problem in $4+1$ dimensional noncommutative spacetime in the first order approximation of noncommutative parameter. The case of higher dimensions $D\geq 4$ is also discussed.