2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/201657We examine both quantum and classical versions of the problem of spin evolution in a slowly varying magnetic field. Main attention is given to the first- and second-order adiabatic corrections in the case of in-plane variations of the magnetic field. While the first-order correction relates to the adiabatic Berry phase and Coriolis-type lateral deflection of the spin, the second-order correction is shown to be responsible for the next-order geometric phase and in-plain deflection. A comparison between different approaches, including the exact (non-adiabatic) geometric phase, is presented.10 pages, 1 figure, to appear in Phys. Lett. AQuantum PhysicsOther Condensed Mattertext