In physics, consideration of phenomena in one or two space dimensions (1 + 1 or 2 + 1 space-time dimensions) is often regarded as a useful step toward understanding them in three space dimensions (3 + 1 space-time dimensions). This article presents the basic dynamics of a neutron with a magnetic moment in the presence of certain electromagnetic fields in 2 + 1 space-time dimensions by using a polar coordinate system. We illustrate this approach with two simple instances within the theory of the Dirac equation: (i) a (neutron) harmonic oscillator, and (ii) a particular kind of hydrogen atom-like system; wherein the Aharonov–Casher discrete states are exemplified within the framework of relativistic quantum mechanics.

中文翻译：

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中子与电磁场的相互作用：一种教学方法

在物理学中，在一个或两个空间维度（1 + 1或2 +1时空维度）中考虑现象通常被视为在三个空间维度（3 +1时空维度）中理解现象的有用步骤。本文通过极坐标系统介绍了在2 + 1时空维度上存在某些电磁场的情况下具有磁矩的中子的基本动力学。我们用狄拉克方程的理论中的两个简单实例来说明这种方法：（i）一个（中子）谐波振荡器，和（ii）一种特殊的类氢原子系统；其中，Aharonov–Casher离散态在相对论量子力学的框架内得到例证。