The usual quantitative condition has been widely used in the practical
applications of the adiabatic theorem. However, it had never been proved to be
sufficient or necessary before. It was only recently found that the
quantitative condition is insufficient, but whether it is necessary remains
unresolved. In this letter, we prove that the quantitative condition is
necessary in guaranteeing the validity of the adiabatic approximation.Comment: 4 pages,1 figue