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I understand it's an approach to calculating the band structure in solids.

**[(-ħ**

^{2}/2m)∇^{2}+ V(r)]Ψ = EΨCoulomb potential for a hydrogen atom:

**V(r) = -e**

^{2}/4πϵrRight now I'm imagining a 2D case where hydrogen atoms are lined up in a row. The electron in question experiences a coulomb potential from other atoms in the crystal.

**∑**

_{i}V(r - R_{i})This will tell us what all the other coulomb potentials are. When we expand it out we get V(r) [

*the coulomb potential the electron experiences from it's own nucleus*] and V(Ri) -

*[the potential the electron experiences from the nucleus of nearby atoms*]

**[(-ħ**

^{2}/2m)∇2 + ∑_{i}V(r - R_{i})] = EΨThis only describes what the energy of 1 electron is. From here I get a bit confused with it all.