Non-anti-hermitian quaternionic quantum mechanics

TL;DR

This paper investigates the conditions under which Ehrenfest's theorem holds in non-anti-hermitian quaternionic quantum mechanics, revealing its relation to non-hermitian quantum mechanics and implications for physical problem modeling.

Contribution

It analyzes the validity of Ehrenfest's theorem in non-anti-hermitian QQM and establishes its connection to non-hermitian quantum mechanics.

Findings

Ehrenfest's theorem validity depends on specific conditions in non-anti-hermitian QQM.

Non-anti-hermitian QQM is related to non-hermitian quantum mechanics.

The study clarifies the physical implications of non-anti-hermitian quaternionic formulations.

Abstract

The breakdown of Ehrenfest's theorem imposes serious limitations on quaternionic quantum mechanics (QQM). In order to determine the conditions in which the theorem is valid, we examined the conservation of the probability density, the expectation value and the classical limit for a non-anti-hermitian formulation of QQM. The results also indicated that the non-anti-hermitian quaternionic theory is related to non-hermitian quantum mechanics, and thus the physical problems described with both of the theories should be related.