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

• URL: http://arxiv.org/abs/2502.16165v2
• Date: Fri, 28 Mar 2025 21:01:18 GMT
• Title: Dirac-isotonic oscillators in (1 + 1) and (2 + 1) dimensions
• Authors: Aritra Ghosh, Bhabani Prasad Mandal,
• Abstract summary: We show that a Dirac oscillator in $(2+1)$ dimensions can be mapped to an anti-Jaynes-Cummings-like Hamiltonian.<n>We describe exact solutions of these generalized systems and also present their non-relativistic limits.
• Score: 7.00493617363289
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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