Quaternionic Diffusion by a Potential Step

TL;DR

This paper explores how quaternionic quantum mechanics differs from complex quantum mechanics in wave packet diffusion at a potential step, highlighting significant differences in group velocity and reflection/transmission times that could inspire future experiments.

Contribution

It provides a detailed analysis of wave packet behavior in quaternionic quantum theory, emphasizing differences from complex theory in potential step scenarios.

Findings

Distinct group velocity behavior in quaternionic vs. complex formulations

Different reflection and transmission times observed

Potential for experimental verification of quaternionic effects

Abstract

In looking for qualitative differences between quaternionic and complex formulations of quantum physical theories, we provide a detailed discussion of the behavior of a wave packet in presence of a quaternionic time-independent potential step. In this paper, we restrict our attention to diffusion phenomena. For the group velocity of the wave packet moving in the potential region and for the reflection and transmission times, the study shows a striking difference between the complex and quaternionic formulations which could be matter of further theoretical discussions and could represent the starting point for a possible experimental investigation.