I'm trying to understand the tight binding method but I'm struggling with a lot of the mathematical formalism. A lot of the mathematical formalism I read jumps into explaining it a few too many steps ahead of where my understanding is.(adsbygoogle = window.adsbygoogle || []).push({});

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

[(-ħ^{2}/2m)∇^{2}+ V(r)]Ψ = EΨ

Coulomb potential for a hydrogen atom:

V(r) = -e^{2}/4πϵr

Right 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})] = EΨ

This only describes what the energy of 1 electron is. From here I get a bit confused with it all.

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# I Tight Binding Method

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