Quaternioninc Dirac Scattering

TL;DR

This paper explores how quaternionic potentials affect Dirac particle scattering, revealing unique phenomena like total transmission and the need for operator measurements to detect quaternionic effects.

Contribution

It introduces a quaternionic generalization of Dirac scattering solutions, uncovering new effects such as total transmission with pure quaternionic potentials.

Findings

Quaternionic solutions extend complex solutions with additional diffusion.

Total transmission occurs for pure quaternionic potentials.

Reflection and transmission rates alone cannot detect quaternionic potentials.

Abstract

The scattering of a Dirac particle has been studied for a quaternionic potential step. In the potential region an additional diffusion solution is obtained. The quaternionic solution which generalizes the complex one presents an amplification of the reflection and transmission rates. A detailed analysis of the quaternionic spinorial velocities sheed new light on the additional solution. For pure quaternionic potentials, the interesting and surprising result of total transmission is found. This suggests that the presence of pure quaternionic potentials cannot be seen by analyzing the reflection or transmission rates. It has be observed by measuring the mean value of some operator.