  We study Anderson localization in a disordered potential combined with an
inhomogeneous trap. We show that the spectrum displays both localized and
extended states, which coexist at intermediate energies. In the region of
coexistence, we find that the extended states result from confinement by the
trap and are weakly affected by the disorder. Conversely, the localized states
correspond to eigenstates of the disordered potential, which are only affected
by the trap via an inhomogeneous energy shift. These results are relevant to
disordered quantum gases and we propose a realistic scheme to observe the
coexistence of localized and extended states in these systems.
