Quantum adiabatic theorem (II): approximation and condition for application

Recent research on the quantum adiabatic theorem and the conditions for its applicationare briefly reviewed. The inconsistencies of the theorem and adiabatic approximation discussed in the recent literature are described. The author′s points of view are presented in a way different from those in the current literature. The existence of the inconsistency is confirmed, while the consistency of the so－called vanishing quantum geometric phase is shown to be due to misunderstanding about the phase of the instantaneous eigenfunction of the Hamiltonian.