When going from the bulk solid to a thin-film of nanometer dimensions,
the electronic structure becomes discretized in the perpendicular dir
ection. These discrete states, also called thin film states and quantu
m well states, are clearly distinguished in photoemission experiments
as two-dimensional and thickness-dependent modulations of the bulk spe
ctra, although their observation is limited to highly perfect epitaxia
l systems. The photoemission data are well explained in the framework
of a simple model for the electron wave function in a quantum well sta
te. Thin film states become spin-polarized when growing on ferromagnet
ic substrates. Furthermore, spin-polarized, thickness-dependent modula
tions at a given energy lead to spin-dependent periodic oscillations o
f the density of states as a function of thickness, which are found to
be responsible for the oscillatory coupling observed in magnetic mult
ilayers.