Quaternionic Quantum Mechanics: the Particles, their q-Potentials and Mathematical Electron Model

TL;DR

This paper explores quaternionic quantum mechanics across scales, introducing a new mathematical electron model based on quaternion relations, velocity postulate, and continuum concepts at the Planck level.

Contribution

It presents a novel quaternionic framework for quantum processes, incorporating new symmetrization and velocity postulates, and develops a mathematical electron model.

Findings

Quaternionic descriptions apply from Planck to macro scales.

New quaternionic electron model based on deformation potentials.

Key role of quaternion velocity and symmetrization in quantum descriptions.

Abstract

In this work we show the quaternionic quantum descriptions of physical processes from the Planck to macro scale. The results presented here are based on the concepts of the Cauchy continuum and the elementary cell at the Planck scale. The symmetrization of quaternion relations and the postulate of quaternion velocity have been crucial in the present development. The momentum of the expansion and compression is the consequence of the scalar term in the quaternionic deformation potential.