Quantum mechanics with quaternionic mass

TL;DR

This paper explores quaternionic mass in quantum mechanics, deriving modified Klein-Gordon and Telegraph equations, revealing new mass components, and analyzing particle interactions with electromagnetic fields.

Contribution

It introduces quaternionic mass into quantum mechanics, deriving new equations and analyzing particle-field interactions with novel mass components.

Findings

Quaternionic mass leads to Klein-Gordon and Telegraph equations.

Particles with quaternionic mass exhibit unique energy interactions.

Electromagnetic coupling introduces additional energy terms.

Abstract

Quantum mechanics with quaternionic mass is considered. The momentum eigen-value equation with quaternionic mass yields the Klein-Gordon equation with a mass consisting of longitudinal and traverse masses. The scalar field total mass is found to be a sum of these masses. This field appears to be connected with two subfields conserving linear momentum. It is found that a particle with real mass satisfies the quantum Telegraph equation, whereas that one with quaternionic mass satisfies the Klein-Gordon equation. A quantum force acting on the particle is found to be proportional to its velocity. When the particle field is coupled to an electromagnetic field, an additional term in the particle's energy appears reflecting the interaction of the particle's angular momentum with the magnetic field.