Degeneracy of Schrodinger equation with potential $1/r$ in $d$-dimensions

TL;DR

This paper explores the degeneracy symmetry of the hydrogen atom in arbitrary dimensions using group theory, specifically the irreducible representations of SO(d+1), to derive the energy spectrum and degeneracy.

Contribution

It introduces a group-theoretic approach to analyze the hydrogen atom in d-dimensions, identifying SO(d+1) as the energy spectrum generating group.

Findings

Derived the energy spectrum for hydrogen in d-dimensions.

Calculated the degeneracy of energy levels.

Established SO(d+1) as the symmetry group responsible for degeneracy.

Abstract

Using the irreducible representations of the group $SO(d+1)$, we discuss the degeneracy symmetry of hydrogen atom in $d$-dimensions and calculate its energy spectrum as well as the correspouding degeneracy. We show that $SO(d+1)$ is the energy spectrum generating group