  We study the family of Hamiltonians which corresponds to the adjacency
operators on a percolation graph. We characterise the set of energies which are
almost surely eigenvalues with finitely supported eigenfunctions. This set of
energies is a dense subset of the algebraic integers. The integrated density of
states has discontinuities precisely at this set of energies. We show that the
convergence of the integrated densities of states of finite box Hamiltonians to
the one on the whole space holds even at the points of discontinuity. For this
we use an equicontinuity-from-the-right argument. The same statements hold for
the restriction of the Hamiltonian to the infinite cluster. In this case we
prove that the integrated density of states can be constructed using local data
only. Finally we study some mixed Anderson-Quantum percolation models and
establish results in the spirit of Wegner, and Delyon and Souillard.
