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arXiv:1709.09941 · Advances in High Energy Physics

Scattering Study of Fermions due to Double Dirac Delta Potential in Quaternionic Relativistic Quantum Mechanics

HASSAN HASSANABADI, Hadi Sobhani, Won Sang Chung

Published Jan 1, 2018• 18 citations
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Abstract

We have studied the scattering problem of relativistic fermions from a quaternionic double Dirac delta potential. We have used Dirac equation in the presence of the scalar and vector potentials in the quaternionic formalism of relativistic quantum mechanics to study the problem. The wave functions of different regions have been derived. Then, using the reflection coefficient, transmission coefficient, and the continuity equation, the scattering problem has been investigated in detail. It has been shown that we have faced some fluctuations in the reflection and transmission coefficients.

DOI
10.1155/2018/8124073

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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.
Abstract In this paper, by introducing the q -deformed delta function, the Dirac equation for a fermion in the presence of Dirac delta scalar and vector potential is developed. Then, considering the boundary condition and the effect of the q -deformed Dirac delta potential, the scattering state is investigated. Further, the reflection and transmission coefficients are determined. Moreover, the effect of the q -parameter and the potential coefficient on the reflection and transmission coefficients is reported.
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.
The Dirac delta function potential is considered within the real Hilbert space approach for complex wave functions, as well as quaternionic wave functions. As has been previously determined, the real Hilbert space approach enables the possibility of self-interacting physical systems. The self-interaction precludes confining states, and also imposes non-stationary quantum states, both of them representing novel situations that cannot be observed in terms of quantum wave functions. These results remark the differences between quaternionic quantum mechanics ($\mathbbm H$QM) and complex quantum mechanics ($\mathbbm C$QM), and also establish a method of solving the wave equation that may be applied to a variety of different cases.