How to determine band structure (E(k)) of a one dimensional crystal?

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Discussion Overview

The discussion revolves around determining the band structure (E(k)) of a one-dimensional crystal, specifically focusing on a system with two atoms (A and B) spaced a/2 units apart. The inquiry is about the algorithmic approach to calculate this band structure by hand, with an emphasis on the tight-binding model involving one orbital per atom and nearest neighbor hopping.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • Simon seeks guidance on the algorithm to determine the band structure for a one-dimensional crystal, expressing uncertainty about where to start.
  • Simon specifies that the crystal consists of two atoms, A and B, spaced a/2 units apart.
  • Another participant inquires whether Simon is using the tight-binding model with one orbital per atom and nearest neighbor hopping, which Simon confirms.

Areas of Agreement / Disagreement

The discussion remains unresolved, with Simon looking for specific guidance on the algorithm without a consensus on the approach yet.

Wicked85
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Hi!
I'm new to the physics forum but I've read a little bit and I'm impressed with the knowledge a lot of people have here. I've tried searching for any topic on my question without any luck.

My question is simply what the algorithm is to determine the band structure for a one dimensional crystal (I'm supposed to do it by hand), this seems fairly easy but I just don't know where to start!

Any help would be GREATLY appreciated! :)
Thanks!
Simon
 
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I should add that it's two atoms in the chrystal, A & B spaced a/2 units apart.
 
Are you doing tight-binding with one orbital per atom and only nearest neighbor hopping?
 
Yes, that's correct. Any ideas? :)
 

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