2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104694We review mathematical results concerning exponentially small corrections to adiabatic approximations and Born--Oppenheimer approximations.To appear in the proceedings of the 2005 International Conference on Differential Equations and Mathematical Physics, University of Alabama, BirminghamMathematical Physics81Q05, 81Q15Recent Results on Non--Adiabatic Transitions in Quantum Mechanicstext