 Nearly free electron model

The nearly-free electron model treats a weak periodic potential by degenerate perturbation theory. At a Bragg crossing, a Fourier coefficient $V_n$ couples the two degenerate plane waves and opens an energy gap of width $2|V_n|$.

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.