Empty lattice approximation: Difference between revisions

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==Scattering and periodicity==

[[Image:1D-Empty-Lattice-Approximation.svg|thumb|400px|Free electron bands in a one dimensional lattice]]

The periodic potential of the lattice must be weak because otherwise the electrons wouldn't be free. The strength of the scattering mainly depends on the 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]]. One thing is clear for currently known 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 (periodic potential)|particle in a one-dimensional lattice]], like the [[Kronig-Penney model]], it is easy to substitute the values for the potential and the size of the potential well.<ref name=Kittel>

{{cite book |author=C. Kittel |title=Introduction to Solid State Physics |year= 1953-1976 |publisher=Wiley & Sons |isbn=0-471-49024-5 }}

</ref>