Virial theorem and generalized momentum in quaternic quantum mechanics

TL;DR

This paper extends quaternionic quantum mechanics by establishing the Virial theorem, Lorentz force, magnetic monopole, and redefining expectation values, demonstrating its consistency with standard complex quantum mechanics.

Contribution

It introduces new theoretical results in quaternionic quantum mechanics, including the Virial theorem and magnetic monopole, enhancing its foundational framework.

Findings

Virial theorem established in quaternionic quantum mechanics

Existence of quaternionic magnetic monopole demonstrated

Redefinition of expectation values in quaternionic context

Abstract

After a review on recent results on quaternic quantum mechanics ($\mathbb{H}$QM), we present further consistency tests that reinforce its compatibility with the usual complex quantum mechanics ($\mathbb{C}$QM). The novel results comprises the Virial theorem, the quantum quaternic Lorentz force, the existence of a quaternic magnetic monopole and the redefinition of the expectation value.