We report an angle resolved photoemission study of quantum size effects observed in the electronic structure of pseudomorphic Cu(100) films. The 3d band of a one-layer film exhibits an 80% reduction in its perpendicular dispersion and a 10% reduction in its parallel dispersion. The perpendicular dispersion of the 3 d band evolves rapidly with increasing film thickness, since the 3 d electrons are strongly localized on the ion cores. Quantum-well resonances are produced due to the discretization of the perpendicular wave vector in the s,p band. They produce oscillations in the Fermi level intensity as they disperse through it when the film thickness is increased. The observed oscillation period of approximately six layers matches that of oscillations in the magnetic exchange coupling between ferromagnetic Co films separated by Cu spacer layers. The connection of the quantum-well states to bulk electronic structure is determined by comparing oscillation amplitudes for two different photon energies.