  The Schroedinger equation with a potential periodically varying in time is
used to model adiabatic quantum pumps. The systems considered may be either
infinitely extended and gapped or finite and connected to gapless leads.
Correspondingly, two descriptions of the transported charge, one relating to a
Chern number and the other to a scattering matrix, have been available for some
time. Here we generalize the first one and establish its equivalence to the
second.
