Using inverse photoemission and photoemission we find that the bulk bands become discretized in highly perfect layer structures, such as Cu on fcc Co(100), Cu on fcc Fe(100), Ag on bcc Fe(100), Au on bcc Fe (100), fcc Co on Cu(100), and bcc Fe on Au(100). The electronic structure is analyzed in the framework of quantum-well states consisting of bulk Bloch functions modulated by an envelope function. The wavelength of the envelope function is determined from the lambda/2 interferometer fringes produced by the periodic appearance of quantum-well states with increasing film thickness. Using k conservation, one obtains an absolute measurement of the band dispersion for the s,p bands of Fe, Cu, Ag, and Au. Quantum-well states at the Fermi level are found to be closely connected with oscillatory magnetic coupling in superlattices. They are spin polarized, even in noble metals, due to the spin-dependent band structure of the confining ferromagnet. The oscillation period is half the wavelength of the envelope function. The corresponding wave vector is given by the Fermi wave vector and by the wave vector of the nearest s,p band edge via 2(k(edge) - k(F)). This turns out to be equivalent to Ruderman-Kittel-Kasuya-Yosida theory.