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Quantum well states are believed to underlie the magnetic behavior of the layered metallic nanostructures now under intense development for advanced data storage and memory applications, so understanding them is a major thrust of magnetic-materials research. In a metal, an electron wave function can be represented by a short-wavelength component that is modulated by an envelope with a longer wavelength. In a large sample, the allowed electron energies fall into a series of bands within which the energy is quasi-continuous, but as the dimensions shrink, the allowed energies become widely separated and few in number. For a film, which is thin in only one direction, the energy is quantized in this way for travel perpendicular to the film surface and is continuous for travel parallel to the surface. In the model for quantum well states, the envelope functions must fit an integer number of half-wavelengths into roughly the film thickness.