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arXiv · 2101.03922

Dirac Hamiltonian in a supersymmetric framework

Bijan Bagchi·Rahul Ghosh
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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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Bijan Bagchi, Rahul Ghosh. 2021-06-29. Dirac Hamiltonian in a supersymmetric framework. https://doi.org/10.1063/5.0043854

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