  The quantum adiabatic theorem states that if a quantum system starts in an
eigenstate of the Hamiltonian, and this Hamiltonian varies sufficiently slowly,
the system stays in this eigenstate. We investigate experimentally the
conditions that must be fulfilled for this theorem to hold. We show that the
traditional adiabatic condition as well as some conditions that were recently
suggested are either not sufficient or not necessary. Experimental evidence is
presented by a simple experiment using nuclear spins.
