# Quaternionic quantum particles: new solutions

## TL;DR

This paper explores a new approach to solving the quaternionic Schrödinger equation, presenting solutions for free particles and scattering, thereby expanding the understanding of quaternionic quantum mechanics.

## Contribution

It introduces a second method for solving the quaternionic Schrödinger equation and provides explicit solutions for free particles and scattering scenarios.

## Key findings

- Derived new quaternionic free particle solutions
- Analyzed quaternionic particle scattering through scalar barriers
- Extended quaternionic quantum mechanics framework

## Abstract

If $\Psi$ is a quaternionic wave function, then $i\Psi\neq \Psi i$. Thus, there are two versions of the quaternionic Schr\"odinger equation (QSE). In this article, we present the second possibility for solving the QSE, following on from a previous article. After developing the general methodology, we present the quaternionic free particle solution and the scattering of the quaternionic particle through a scalar barrier.