2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/92715We discuss adiabatic quantum phenomena at a level crossing. Given a path in the parameter space which passes through a degeneracy point, we find a criterion which determines whether the adiabaticity condition can be satisfied. For paths that can be traversed adiabatically we also derive a differential equation which specifies the time dependence of the system parameters, for which transitions between distinct energy levels can be neglected. We also generalize the well-known geometric connections to the case of adiabatic paths containing arbitrarily many level-crossing points and degenerate levels.7 pages, 6 figures, RevTeX4, changes requested by Phys. Rev. AQuantum PhysicsOther Condensed Mattertext