$SO(4)$ Symmetry in Hydrogen Atom with Spin
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866914758325698560 |
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| author | Fan, Xing-Yan Xie, Xiang-Ru Li, Sheng-Ming Chen, Jing-Ling |
| author_facet | Fan, Xing-Yan Xie, Xiang-Ru Li, Sheng-Ming Chen, Jing-Ling |
| contents | As the simplest atom in nature, the hydrogen atom has been explored thoroughly from the perspective of non-relativistic quantum mechanics to relativistic quantum mechanics. Among the research on hydrogen atom, its energy level is the most basic, which can be obtained more conveniently predicated on the $SO(4)$ symmetry than the wave-equation resolution. Moreover, ``spin'' is another indispensable topic in quantum mechanics, appearing as an intrinsic degree of freedom. In this work, we generalize the quantum Runge-Lenz vector to a spin-dependent one, and then extract a novel Hamiltonian of hydrogen atom with spin based on the requirement of $SO(4)$ symmetry. Furthermore, the energy spectrum of hydrogen atom with spin potentials is also determined by the remarkable approach of $SO(4)$ symmetry. Our findings extend the ground of hydrogen atom, and may contribute to other complicated models based on hydrogen atom. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11437 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $SO(4)$ Symmetry in Hydrogen Atom with Spin Fan, Xing-Yan Xie, Xiang-Ru Li, Sheng-Ming Chen, Jing-Ling Quantum Physics As the simplest atom in nature, the hydrogen atom has been explored thoroughly from the perspective of non-relativistic quantum mechanics to relativistic quantum mechanics. Among the research on hydrogen atom, its energy level is the most basic, which can be obtained more conveniently predicated on the $SO(4)$ symmetry than the wave-equation resolution. Moreover, ``spin'' is another indispensable topic in quantum mechanics, appearing as an intrinsic degree of freedom. In this work, we generalize the quantum Runge-Lenz vector to a spin-dependent one, and then extract a novel Hamiltonian of hydrogen atom with spin based on the requirement of $SO(4)$ symmetry. Furthermore, the energy spectrum of hydrogen atom with spin potentials is also determined by the remarkable approach of $SO(4)$ symmetry. Our findings extend the ground of hydrogen atom, and may contribute to other complicated models based on hydrogen atom. |
| title | $SO(4)$ Symmetry in Hydrogen Atom with Spin |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2404.11437 |