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arXiv · 2502.16165

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

Aritra Ghosh·Bhabani Prasad Mandal
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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.

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Aritra Ghosh, Bhabani Prasad Mandal. 2025-02-22. Dirac-isotonic oscillators in (1 + 1) and (2 + 1) dimensions. https://doi.org/10.1016/j.physleta.2025.130488

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