2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97871We propose a new formula for the adiabatic Berry phase which is based on phase-space formulation of quantum mechanics. This approach sheds a new light into the correspondence between classical and quantum adiabatic phases -- both phases are related with the averaging procedure: Hannay's angle with averaging over the classical torus and Berry's phase with averaging over the entire classical phase space with respect to the corresponding Wigner function. Generalizations to the non-abelian Wilczek--Zee case and mixed states are also included.5 pagesQuantum Physicstext