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.