On the adiabatic theorem of quantum mechanics

Let H(t) be a Hamiltonian whose spectrum has for all t a finite number of disjoint components σsub(j)(t). It is proved than when the change of H(t) is made infinitely slow the system, when started from a state corresponding to σsub(k)(O), passes through states corresponding to σsub(k)(t), for all t. (author)