Dirac-isotonic oscillators in (1 + 1) and (2 + 1) dimensions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913771338858496 |
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| author | Ghosh, Aritra Mandal, Bhabani Prasad |
| author_facet | Ghosh, Aritra Mandal, Bhabani Prasad |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16165 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dirac-isotonic oscillators in (1 + 1) and (2 + 1) dimensions Ghosh, Aritra Mandal, Bhabani Prasad Quantum Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems 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. |
| title | Dirac-isotonic oscillators in (1 + 1) and (2 + 1) dimensions |
| topic | Quantum Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2502.16165 |