  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.
