Abstract
We discuss the Dirac oscillator in (1+1) and (2+1) dimensions and generalize it in the spirit of the isotonic oscillator using supersymmetric quantum mechanics. In (1+1) dimensions, the Dirac oscillator returns to the quantum harmonic oscillator in the non-relativistic limit, while its generalization maps to the isotonic oscillator. We describe exact solutions of these generalized systems and also present their non-relativistic limits. Finally, based on supersymmetric quantum mechanics, we show that a generalized Dirac oscillator in (2+1) dimensions can be mapped to an anti-Jaynes-Cummings-like Hamiltonian in which the spin operators couple with the supercharges.