  We examine the quantitative condition which has been widely used as a
criterion for the adiabatic approximation but was recently found insufficient.
Our results indicate that the usual quantitative condition is sufficient for a
special class of quantum mechanical systems. For general systems, it may not be
sufficient, but it along with additional conditions is sufficient. The usual
quantitative condition and the additional conditions constitute a general
criterion for the validity of the adiabatic approximation, which is applicable
to all $N-$dimensional quantum systems. Moreover, we illustrate the use of the
general quantitative criterion in some physical models.
