In this thesis, we would like to study on the consistency of the adiabatic theorem. We analyze and reexamine the validity of the adiabatic approximation, and in particular the necessity and insufficiency of the traditional adiabatic conditions. We will argue that the adiabatic condition is insufficent but it is necessary in guaranteeing the validity of the adiabatic approximation. We also introduce different examples of two-level systems which are exactly solvable to demonstrate the necessity and insufficiency of the adiabatic conditions, as well as the inconsistency of the adiabatic approximation.

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