We explore the non-commutative (NC) effects on the energy spectrum of a two-dimensional hydrogen atom. We consider a confined particle in a central potential and study the modified energy states of the hydrogen atom in both coordinates and momenta of non-commutativity spaces. By considering the Rashba interaction, we observe that the degeneracy of states can also be removed due to the spin of the particle in the presence of NC space. We obtain the upper bounds for both coordinates and momenta versions of NC parameters by the splitting of the energy levels in the hydrogen atom with Rashba coupling. Finally, we find a connection between the NC parameters and Lorentz violation parameters with the Rashba interaction.

中文翻译：

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非对易空间中具有 Rashba 耦合的二维氢原子的能级分裂

我们探索了对二维氢原子能谱的非交换 (NC) 效应。我们考虑中心势中的受限粒子，并研究氢原子在非交换空间的坐标和动量中的修正能态。通过考虑 Rashba 相互作用，我们观察到由于在 NC 空间存在下粒子的自旋，状态的简并性也可以消除。我们通过使用 Rashba 耦合分裂氢原子中的能级来获得 NC 参数的坐标和动量版本的上限。最后，我们通过 Rashba 交互找到了 NC 参数和洛伦兹违规参数之间的联系。