$SO(4)$ Symmetry in Hydrogen Atom with Spin
Autor: | Fan, Xing-Yan, Xie, Xiang-Ru, Li, Sheng-Ming, Chen, Jing-Ling |
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Rok vydání: | 2024 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | 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. Comment: 7 pages, 0 figure |
Databáze: | arXiv |
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