The model of a planar atom which possesses a nonvanishing electric dipole moment interacting with magnetic fields in a specific setting is studied. Energy spectra of this model and its reduced model, which is the limit of cooling down the atom to the negligible kinetic energy, are solved exactly. We show that energy spectra of the reduced model cannot be obtained directly from the full ones by taking the same limit. In order to get the energy spectra of the reduced model from the full model, we must regularize energy spectra of the full model properly when the limit of the negligible kinetic energy is taken. It is one of the characteristics of the Chern–Simons quantum mechanics. Besides this, the canonical angular momentum of the reduced model will take fractional values although the full model can only take integers. It means that it is possible to realize the Chern–Simons quantum mechanics and fractional angular momentum simultaneously by this model.

中文翻译：

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Chern-Simons 量子力学和原子系统中的分数角动量

研究了具有非零电偶极矩的平面原子在特定环境下与磁场相互作用的模型。该模型的能谱及其简化模型，即将原子冷却到可忽略的动能的极限，得到了精确求解。我们表明，通过采用相同的限制，不能直接从完整模型中获得简化模型的能谱。为了从全模型中得到简化模型的能谱，在取可忽略动能极限时，必须对全模型的能谱进行适当的正则化。这是陈-西蒙斯量子力学的特征之一。除此之外，简化模型的规范角动量将采用小数值，尽管完整模型只能采用整数。