Abstract
In this work, we have obtained the solutions of a massless fermion which is under the external magnetic field around a cosmic string for specific three potential models using supersymmetric quantum mechanics. The constant magnetic field, energy-dependent potentials, and position-dependent mass models are investigated for the Dirac Hamiltonians, and an extension of these three potential models and their solutions is also obtained. The energy spectrum and potential graphs for each case are discussed for the α deficit angle.
Highlights
The massless Dirac character of the low energy electrons moving has attracted much interest in physics due to the graphene’s important electronic properties [1]
There are a series of studies on the interaction of graphene electrons in perpendicular magnetic fields which have been carried out in order to find a way for confining the charges [2, 3]
Lie algebraic approaches [11], a hydrogen atom in the background of an infinitely thin cosmic string [12], scalar particle dynamics in gravity’s rainbow through the space-time of a cosmic string [13], and N = 2 supersymmetric approach to cosmic string dynamics [14] are some recent studies about the topic
Summary
The massless Dirac character of the low energy electrons moving has attracted much interest in physics due to the graphene’s important electronic properties [1]. The context of SUSY QM was first studied by Witten [17] and Cooper and Freedman [18] This theory, which still attracts much attention today, has application in optics [19] and biophysics [20]; it has a very important place in both relativistic [21] and nonrelativistic quantum mechanics [22, 23]. Their energy and potential function graphs are shown.
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