Some non-relativistic implications of hydrogenic solutions to angular momenta

TL;DR

This paper explores mathematical identities related to angular momentum in hydrogen-like systems, aiding approximation methods by providing derivations of key commutative relations.

Contribution

It offers derivations of angular momentum identities relevant to hydrogenic solutions, enhancing understanding of non-relativistic quantum systems.

Findings

Provides explicit derivations of angular momentum relations.

Clarifies the role of these identities in approximation methods.

Facilitates comparison between exact solutions and approximations.

Abstract

The intention of this paper is to provide solutions to commutative relations relevant to calculations regarding the hydrogen atom (or similar monoelectronic systems). Though exact solutions exist to these systems, the value to approximation methods stems from the ability to conveniently parse physical non-sense by comparison with these identities. A derivation accompanies each identity.