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Physics
Atomic and Condensed Matter
Understand Tight Binding Method: Coulomb Potential, 2D Case & More
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[QUOTE="says, post: 6037757, member: 517464"] 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. I understand it's an approach to calculating the band structure in solids. [B][(-ħ[SUP]2[/SUP]/2m)∇[SUP]2[/SUP] + V(r)]Ψ = EΨ[/B] Coulomb potential for a hydrogen atom: [B]V(r) = -e[SUP]2[/SUP]/4πϵr[/B] 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. [B]∑[SUB]i[/SUB] V(r - R[SUB]i[/SUB])[/B] This will tell us what all the other coulomb potentials are. When we expand it out we get V(r) [[I]the coulomb potential the electron experiences from it's own nucleus[/I]] and V(Ri) - [I][the potential the electron experiences from the nucleus of nearby atoms[/I]] [B][(-ħ[SUP]2[/SUP]/2m)∇2 + ∑[SUB]i[/SUB] V(r - R[SUB]i[/SUB])] = EΨ[/B] This only describes what the energy of 1 electron is. From here I get a bit confused with it all. [/QUOTE]
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Physics
Atomic and Condensed Matter
Understand Tight Binding Method: Coulomb Potential, 2D Case & More
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