Comment on the adiabatic condition

The experimental observation of effects due to Berry's phase in quantum sys tems is certainly one of the most impressive demonstrations of the correctn ess of the superposition principle in quantum mechanics. Since Berry's orig inal paper in 1984, the spin 1/2 coupled with a rotating external magnetic field has been one of the most studied models where those phases appear. We also consider a special case of this soluble model. A detailed analysis of the coupled differential equations and comparison with exact results teach us why the usual procedure (of neglecting nondiagonal terms) is mathematic ally sound. (C) 2000 American Association of Physics Teachers.