In solid-state physics, crystals are usually assumed to be large enough that the influence of finite dimensions on their electronic structure is negligible compared to the effects of the periodic potential produced by the regular arrangement of the ion cores. The energy of a nearly free valence-band electron in a metal can then simply be described by its dependence on the wave vector k = (2π/λ)e, where e is a unit vector in the direction of propagation of the electron and λ is its wavelength.

When one or more dimensions of the crystal approach interatomic distances or the electron's wavelength, however, the electron feels the effects of the crystal boundaries in addition to the periodic potential. The potential outside the solid is drastically different from the one inside. The influence of the boundaries is clearest in the context of the jellium model, in which...

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