The tight-binding approximation is a method used in solid-state physics to model the electronic band structure of crystalline materials by assuming that electrons can hop between nearby atomic sites. This approach simplifies the complex interactions of electrons in a lattice, allowing for an effective description of their behavior, particularly in narrow energy bands. It connects closely to the Bloch theorem, which states that the wavefunctions of electrons in a periodic potential can be expressed as a product of a plane wave and a function with the periodicity of the lattice.
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