Quantum theory of neutrons in helical magnetic fields

Abstract

The Schr\"odinger equation for a spin-\textonehalf{} neutral particle with a magnetic dipole moment in the presence of a helical periodic magnetic field of arbitrary strength and period is solved exactly. Several interesting physical aspects of the solution emerge. For example, it is found that the energy spectrum has no band structure. It is also found that the spin of the particle rotates in the same way as the magnetic field and that the group velocity behaves quite differently depending on the spin orientations. Several physical applications of these ideas are discussed; in particular, it is shown that these results are equally valid for charged particles, provided their momentum points in the direction of the axis of the helix.