$SO(4)$ Symmetry in Hydrogen Atom with Spin

Autor:	Fan, Xing-Yan, Xie, Xiang-Ru, Li, Sheng-Ming, Chen, Jing-Ling
Rok vydání:	2024
Předmět:	Quantum Physics
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
Externí odkaz:	http://arxiv.org/abs/2404.11437 Zobrazit plný text záznamu View this record from Arxiv