Relativistic scattering of fermions in quaternionic quantum mechanics

Hassan Hassanabadi,Hadi Sobhani,Abhijit Banerjee

doi:10.1140/epjc/s10052-017-5154-5

Hassan Hassanabadi, Hadi Sobhani + Show 1 more

Open Access

https://doi.org/10.1140/epjc/s10052-017-5154-5

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Abstract

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.

Highlights

The mathematical structure of quantum mechanics, one of the fundamental pillars of modern physics of the description of new aspects of nature, consists of Hilbert spaces defined over the field of complex numbers
Physicists have witnessed that the underlying foundations of the theory are enormously successful in describing different quantal phenomena [1–6]
In order to do this, we investigate the quaternionic version of the Dirac equation in Sect

Summary

Introduction

The mathematical structure of quantum mechanics, one of the fundamental pillars of modern physics of the description of new aspects of nature, consists of Hilbert spaces defined over the field of complex numbers. For the first time quantum theory was extended to include the field of quaternions by Hamilton [7,8]. The quaternions can be expressed by extending complex numbers in the following form:. In recent times, scattering for non-relativistic and spinless quantum particles has been studied in [27–29] in the presence of a quaternionic Dirac delta potential in the direction proposed by De Leo [20]. Motivated by the above progress, in this article, we want to investigate the relativistic scattering of fermions in the presence of scalar and vector potentials. In order to do this, we investigate the quaternionic version of the Dirac equation in Sect. We derive the reflection and transmission coefficients to establish the conservation of the current probability in Sect. 4, and in Sect. 5 we present the conclusion of our work

Quaternionic version of the Dirac equation

Investigation of quaternionic Dirac delta scattering

Reflection and transmission coefficients

Conclusion