Energy spectrum of the hydrogen atom in a space with one compactified extra dimension, $\mathbb{R}^3 \times S^1$

TL;DR

This paper explores how a single compactified extra dimension affects the energy spectrum of the hydrogen atom, revealing modifications in energy levels and electron density through numerical analysis.

Contribution

It introduces a numerical method to analyze the hydrogen atom in a space with one compactified extra dimension, highlighting new physical effects.

Findings

Energy levels depend on the compactification radius.

Electron probability density varies with extra dimension size.

Multiple physical effects are identified and discussed.

Abstract

We investigate the consequences of one extra compactified dimension for the energy spectrum of the non-relativistic hydrogen atom with a potential defined by Gauss' law, i.e. proportional to $1/|x|^2$ in non-compactified 4d space. The calculations were performed numerically by diagonalizing the Hamiltonian in two different sets of basis vectors. The energy levels and electron probability density are plotted as a function of the compactification radius. The occurrence of several physical effects is discussed and interpreted.