The Schrödinger equation for a spin‐ 1/2 neutral particle with a magnetic dipole moment interacting with a helical periodic magnetic field of arbitrary strength and period is solved exactly. The solution is easily obtained by exploiting the symmetries of the Hamiltonian and it is expressed in terms of elementary functions. Several interesting physical aspects of the solution emerge. The behavior of the spin, the group velocity, and the effective mass tensor are obtained, yielding some novel and nontrivial results. Because of the mathematical simplicity, this problem is particularly suitable for an elementary graduate course in quantum mechanics.