Dirac-isotonic oscillators in (1 + 1) and (2 + 1) dimensions

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.

v1: Preliminary version; v2: Final version to appear in PLA

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Cited by in corpus (2)

• Comment on "Quantum phase transitions of Dirac particles in a magnetized rotating curved background: Interplay of geometry, magnetization, and thermodynamics"
• Landau levels of a Dirac electron in graphene from non-uniform magnetic fields