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Importing Wikidata short description: "A theoretical electronic band structure model in which the potential is periodic and weak" (Shortdesc helper) |
m link to Introduction to Solid State Physics |
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[[Image:1D-Empty-Lattice-Approximation.svg|thumb|400px|Free electron bands in a one dimensional lattice]]
The periodic potential of the lattice in this free electron model must be weak because otherwise the electrons wouldn't be free. The strength of the scattering mainly depends on the geometry and topology of the system. Topologically defined parameters, like [[Scattering cross-section|scattering]] [[Cross section (physics)|cross sections]], depend on the magnitude of the potential and the size of the [[potential well]]. For 1-, 2- and 3-dimensional spaces potential wells do always scatter waves, no matter how small their potentials are, what their signs are or how limited their sizes are. For a particle in a one-dimensional lattice, like the [[Kronig–Penney model]], it is possible to calculate the band structure analytically by substituting the values for the potential, the lattice spacing and the size of potential well.<ref name=Kittel>
{{cite book |author=C. Kittel |title=[[Introduction to Solid State Physics]] |year= 1953–1976 |publisher=Wiley & Sons |isbn=978-0-471-49024-1 }}
</ref> For two and three-dimensional problems it is more difficult to calculate a band structure based on a similar model with a few parameters accurately. Nevertheless, the properties of the band structure can easily be approximated in most regions by [[Perturbation theory (quantum mechanics)|perturbation methods]].
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