On certain sum rules for the hydrogen atom

TL;DR

This paper critiques recent sum rules for the hydrogen atom, emphasizing the importance of including the continuous spectrum in calculations to ensure accuracy.

Contribution

It clarifies the correct derivation of sum rules by accounting for the continuous spectrum, correcting previous inaccuracies.

Findings

Previous sum rules omitted the continuous spectrum, leading to errors.

Including the continuous spectrum yields correct sum rule results.

Highlights the necessity of considering all spectral components in quantum calculations.

Abstract

We show that some sum rules for the hydrogen atom derived recently are incorrect because the authors did not take into account the continuous part of the spectrum in the sum over intermediate states.