The Simplicity of Perfect Atoms: Degeneracies in Supersymmetric Hydrogen

TL;DR

This paper analyzes supersymmetric hydrogen-like bound states, revealing their spectral similarities to regular hydrogen and classifying their states, with implications for understanding degeneracies and the Lamb shift in supersymmetric contexts.

Contribution

It provides a detailed classification and spectrum calculation of supersymmetric hydrogen, highlighting its degeneracies and relation to non-supersymmetric systems.

Findings

Supersymmetric hydrogen exhibits accidental degeneracy similar to regular hydrogen.

The spectrum is calculated at leading order, showing degeneracy breaking by the Lamb shift.

The study explores limits and connections to other non-relativistic bound states.

Abstract

Supersymmetric QED hydrogen-like bound states are remarkably similar to non-supersymmetric hydrogen, including an accidental degeneracy of the fine structure and which is broken by the Lamb shift. This article classifies the states, calculates the leading order spectrum, and illustrates the results in several limits. The relation to other non-relativistic bound states is explored.