The Nearly Free Electron Model (NFEM) is a theoretical framework used in solid-state physics to describe the electronic properties of metals and some semiconductors. This model extends the free electron model, which treats electrons in a solid as if they were free particles moving in three-dimensional space without any potential energy influence from the atomic lattice of the solid.
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The nearly-free electron model treats a weak periodic potential by degenerate perturbation theory. At a Bragg crossing, a Fourier coefficient couples the two degenerate plane waves and opens an energy gap of width .