Quaternionic eigenvalue problem

TL;DR

This paper explores the quaternionic eigenvalue problem, translating it into real or complex matrix problems, with applications in quaternionic quantum mechanics differential equations.

Contribution

It introduces an isomorphism approach to solve quaternionic eigenvalue problems by relating them to real and complex matrices, enabling new applications.

Findings

Quaternionic eigenvalue problems can be mapped to real/complex matrix problems.

The approach facilitates solving differential equations in quaternionic quantum mechanics.

Potential applications in advanced quantum theories and mathematical physics.

Abstract

We discuss the (right) eigenvalue equation for $\mathbb{H}$, $\mathbb{C}$ and $\mathbb{R}$ linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows to translate the quaternionic problem into an {\em equivalent} real or complex counterpart. Interesting applications are found in solving differential equations within quaternionic formulations of quantum mechanics.