Dirac Hamiltonian in a supersymmetric framework
Abstract
We investigate the most general form of the onedimensional 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 quasiHamiltonian K , defined as the square of H_{D}, to explore the consequences. We show that the diagonal elements of K under a suitable approximation reflect the presence of a superpotential, thus proving a useful guide in unveiling the role of SUSY. For illustrative purposes, we apply our scheme to the transformed onedimensional version of the planar electron Hamiltonian under the influence of a magnetic field. We generate spectral solutions for a class of isochronous potentials.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 July 2021
 DOI:
 10.1063/5.0043854
 arXiv:
 arXiv:2101.03922
 Bibcode:
 2021JMP....62g2101B
 Keywords:

 Quantum Physics;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 To be published in J. Math. Phys. (2021)