  The consistency of quantum adiabatic theorem has been doubted recently. It is
shown in the present paper that the difference between the adiabatic solution
and the exact solution to the Schrodinger equation with a slowly changing
driving Hamiltonian is small; while the difference between their time
derivatives is not small. This explains why substituting the adiabatic solution
back into Schrodinger equation leads to "inconsisitency" of the adiabatic
theorem. Physics is determined completely by the state vector, and not by its
time drivative. Therefore the quantum adiabatic theorem is physically correct.
