Translations between Quaternion and Complex Quantum Mechanics

TL;DR

This paper explores the partial translations between quaternion and complex quantum mechanics, providing a framework to derive quaternion counterparts of standard quantum results, some of which are novel.

Contribution

It introduces a set of translation rules enabling the derivation of quaternion quantum mechanics counterparts from complex quantum mechanics results.

Findings

Established partial translation rules between quaternion and complex quantum mechanics.

Derived quaternion versions of standard quantum mechanical results.

Identified some new quaternion quantum mechanics formulations.

Abstract

While in general there is no one-to-one correspondence between complex and quaternion quantum mechanics (QQM), there exists at least one version of QQM in which a {\em partial} set of {\em translations} may be made. We define these translations and use the rules to obtain rapid quaternion counterparts (some of which are new) of standard quantum mechanical results.