Dimensionality as a Perturbation Parameter in the Generalized Hydrogen Atom

TL;DR

This paper demonstrates that the energy spectrum of the hydrogen atom varies with the number of spatial dimensions, using a perturbation expansion based on the uncertainty principle to confirm this dependence.

Contribution

It introduces a perturbation approach in dimensionality to quantitatively analyze how the hydrogen atom's spectrum depends on spatial dimensions.

Findings

Spectrum depends on the number of dimensions

Perturbation expansion confirms dimensional effects

Uncertainty principle underpins the analysis

Abstract

A recent suggestion has been made that the hydrogen bound state spectrum should not depend on the number of spatial dimensions. It is pointed out here that the uncertainty principle implies that such differences must exist and that a perturbation expansion in the dimensionality parameter yields a precise quantitative confirmation of the effect.