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.
Highlights
Among a lot of mathematical options in physics, quaternions are a famous option
Finkelstein et al discussed a new kind of quantum mechanics by using quaternions [4] or some works which are about using real and complexified quaternions as underlying mathematical structure by adopting a complex geometry to have ability to present a compatible face of quantum mechanics [5, 6]; tunneling phenomena for the relativistic fermions have been studied in the presence of quaternionic step potential [7, 8] and there are a lot of valuable researches in this topic which are mentioned in [9,10,11,12,13,14,15,16,17]
All of them tried to show that we can have a quantum mechanics based on the quaternions
Summary
Among a lot of mathematical options in physics, quaternions are a famous option. Quaternion was initiated by Hamilton for the first time [1,2,3]. Physicists and mathematician have tried to found quantum mechanics on the quaternions. All of them tried to show that we can have a quantum mechanics based on the quaternions. In the rest of the paper, we intend to present quaternionic form of Dirac equation. We want to extend our recent papers [18,19,20,21] to relativistic form as well as having a study of scattering by double Dirac delta potential. In our recent paper [20], we derived the Dirac equation in quaternionic quantum mechanics, in general. Scattering of relativistic fermions due to a single quaternionic Dirac delta function has been studied. It will be shown that scattering due to the quaternionic double Dirac delta function results.
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