Zeeman energy, interference and Neutron Spin Echo: A minimal theory

In some polarized neutron beam experiments, such as Neutron Spin Echo spectroscopy, it is essential to follow exactly the minute changes of the neutron kinetic energy due to interaction with the magnetic fields, e.g. in a spin flip process. It is emphasized that in the Amperian current loop model of microscopic magnetism, shown to be valid by the experiments, the Zeeman energy term can be treated as a bona fide potential energy. This allows us to describe both the spin and the spatial motion of the neutron by using simple notions of wave propagation across potential steps. In this picture Larmor precessions are represented as interference between two Stern-Gerlach states ↑ and ↓. The approach proves to be sufficient for the interpretation of all known polarized neutron beam phenomena, including crystal interferometry. It also leads to the surprising prediction that, as a pure quantum effect, under special circumstances the Larmor precession frequency can be different from its classical value.