We study the electronic properties of a hydrogen-dressed silicon monovacancy as a model of H centers in hydrogenated amorphous silicon (a-Si:H). Using the self-consistent Green's-function technique, we obtain total and local densities of states for the defect, as well as the charge density of defect eigenstates. The hydrogenated vacancy has no states in the band gap and reduces the Si host density of states at both the valence- and conduction-band edge. The SiH bonding character of the defect eigenstates is greatest 4.5 eV below the valence-band edge; however, no sharp H-induced resonance occurs anywhere in the valence or conduction bands. We discuss the importance of including the self-consistent rearrangement of charge around the H atom in obtaining accurate results for the hydrogenated vacancy. Within the context of a recently proposed quantum-well model, we relate the results of our Green's-function calculation to the properties of a-Si:H. Using several simple models (percolation theory, the Anderson model, effective-mass theory), we obtain estimates for the valence- and conduction-band mobility edges. We find that the valence band is much more strongly affected than the conduction band by H disorder, and that H disorder is more important than dihedral-angle disorder in valence-band edge localization. © 1983 The American Physical Society.