Square-well potential in quaternic quantum mechanics

TL;DR

This paper explores the solutions of the one-dimensional square well potential in quaternionic quantum mechanics using a real Hilbert space framework, extending to finite wells and methods to derive quaternionic solutions from complex ones.

Contribution

It introduces a quaternionic quantum mechanics approach to the square well problem and provides a method to generate quaternionic solutions from complex solutions.

Findings

Solutions for the infinite square well in quaternionic quantum mechanics are derived.

Extension to finite square well potential is provided.

A method to generate quaternionic solutions from non-degenerate complex solutions is introduced.

Abstract

The one-dimensional infinite square well is the simplest solution of quantum mechanics, and consequently one of the most important. In this article, we provide this solution using the real Hilbert space approach to quaternic quantum mechanics ($\mathbbm{H}$QM). We further provide the one-dimensional finite as well and a method to generate quaternic solutions from non-degenerate complex solutions.