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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.08726 |
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| _version_ | 1866918019194683392 |
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| author | Salazar-Ramíreza, M. Motab, R. D. Ojeda-Guillén, D. González-Cisneros, A. |
| author_facet | Salazar-Ramíreza, M. Motab, R. D. Ojeda-Guillén, D. González-Cisneros, A. |
| contents | We present exact solutions of the Dirac equation in static curved space-time using two distinct algebraic approaches. The first method employs $su(1,1)$ algebra operators together with the tilting transformation, enabling the derivation of the energy spectrum and eigenfunctions for both the Hydrogen atom and the Dirac-Morse oscillator. The second approach, based on the Schrödinger factorization method, extends the analysis to three representative potentials: the hydrogen atom, the Dirac-Morse oscillator, and a linear radial potential. Although structurally different from those obtained in the first method, the resulting operators in this approach also close the $su(1,1)$ algebra and, through representation theory, yield the corresponding energy spectra and eigenfunctions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08726 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An algebraic solution of Dirac equation on a static curved space-time Salazar-Ramíreza, M. Motab, R. D. Ojeda-Guillén, D. González-Cisneros, A. Quantum Physics Nuclear Theory Atomic Physics We present exact solutions of the Dirac equation in static curved space-time using two distinct algebraic approaches. The first method employs $su(1,1)$ algebra operators together with the tilting transformation, enabling the derivation of the energy spectrum and eigenfunctions for both the Hydrogen atom and the Dirac-Morse oscillator. The second approach, based on the Schrödinger factorization method, extends the analysis to three representative potentials: the hydrogen atom, the Dirac-Morse oscillator, and a linear radial potential. Although structurally different from those obtained in the first method, the resulting operators in this approach also close the $su(1,1)$ algebra and, through representation theory, yield the corresponding energy spectra and eigenfunctions. |
| title | An algebraic solution of Dirac equation on a static curved space-time |
| topic | Quantum Physics Nuclear Theory Atomic Physics |
| url | https://arxiv.org/abs/2505.08726 |