Neutron interaction with electromagnetic fields: A didactic approach

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.