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 deficit angle.

中文翻译：

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宇宙弦时空中无质量费米子行为的扩展

在这项工作中，我们使用超对称量子力学获得了针对特定三个电势模型的无质量费米子的解，该费米子在宇宙弦附近的外部磁场下。研究了狄拉克·哈密顿量的恒定磁场，能量依赖势和位置依赖质量模型，并扩展了这三种势模型及其解。讨论了每种情况下的赤字角的能谱和势图。