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arXiv:1505.01807 · Journal of Physical Mathematics

Quaternionic Dirac Scattering

De Leo, Stefano, Ducati, Gisele, Sergio Giardino

Published Jan 1, 2015• 11 citations
arXivHTMLPDF

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 shed 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 been observed by measuring the mean value of some operator.

DOI
10.4172/2090-0902.1000130

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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 shed 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 been observed by measuring the mean value of some operator.
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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 the 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.
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. PACS. 03.65.Fd – 03.65.Nk I.
In this article, we propose a quaternionic version of the Dirac equation in the presence of scalar and vector potentials. It has been shown that in complex limit of such an equation, the complex version of this equation can be covered. After setting a quaternionic form for the Dirac delta potential, scattering due to the considered interaction has been studied. Wave functions and discontinuity conditions of the problem considered have been derived in detail. Using the continuity equation, we have found a constraint implying the conservation law of the probability current.