Dirac Hamiltonian in a supersymmetric framework

• URL: http://arxiv.org/abs/2101.03922v3
• Date: Tue, 29 Jun 2021 05:43:11 GMT
• Title: Dirac Hamiltonian in a supersymmetric framework
• Authors: Bijan Bagchi and Rahul Ghosh
• Abstract summary: We construct a quasi-Hamiltonian $mathcalK$, defined as the square of $H_D$, to explore the consequences. We show that the diagonal elements of $mathcalK$ under a suitable approximation reflects the presence of a superpotential. For illustrative purpose we apply our scheme to the transformed one-dimensional version of the planar electron Hamiltonian under the influence of a magnetic field.
• Score: 0.4061135251278187
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the most general form of the one-dimensional Dirac Hamiltonian $H_D$ in the presence of scalar and pseudoscalar potentials. To seek embedding of supersymmetry (SUSY) in it, as an alternative procedure to directly employing the intertwining relations, we construct a quasi-Hamiltonian $\mathcal{K}$, defined as the square of $H_D$, to explore the consequences. We show that the diagonal elements of $\mathcal{K}$ under a suitable approximation reflects the presence of a superpotential thus proving a useful guide in unveiling the role of SUSY. For illustrative purpose we apply our scheme to the transformed one-dimensional version of the planar electron Hamiltonian under the influence of a magnetic field. We generate spectral solutions for a class of isochronous potentials.

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