As a two-body system, hydrogen atom with quantum exact solution played an important role for explaining shell structure of multi-electron atoms. Inspired by this, we suggest an alternative interpretation of the integer and fractional quantum Hall effect (QHE) by establishing a direct connection between the exact solutions of a two-dimensional (2D) magnetically trapped electron-pair and the “fundamental” (non-fine) Hall hierarchies of a multi-electron system. We analyze the topology of the exact pair states and report the filling factors of the lowest Landau level based on the exact solutions, which fit the previously and recently reported spectrum of experimental data on the QHE states well and predict some new Hall plateaus for the plateau positions and the eigenenergies reflecting stability and plateau widths. The theoretical prediction associated with the relatively lower minima of the diagonal resistivity is in accurate agreement with the experimental datum spectrum of the fundamental QHE hierarchies.

中文翻译：

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通过电子配对图片对量子霍尔效应的替代解释和预测

作为二体系统，具有量子精确解的氢原子在解释多电子原子的壳结构方面发挥了重要作用。受此启发，我们建议通过在二维 (2D) 磁性俘获电子对的精确解与“基本”（非-很好）多电子系统的霍尔层次结构。我们分析了精确对态的拓扑结构，并根据精确解报告了最低朗道能级的填充因子，这与之前和最近报告的 QHE 态实验数据谱非常吻合，并预测了高原的一些新霍尔高原位置和反映稳定性和平台宽度的特征能量。