Ok, so the “Born–von Karman boundary condition” is helpful in understanding the center area of the brownie. It’s homogenous which is why you can assume the “band index” is periodic / regular and countable. It has to be infinite to work. So, no edges. No edges to the brownie. As I’m interested in the edges, I know where not to look and where something I’m looking at is in the center of the brownie. There’s some important assumptions. https://en.wikipedia.org/wiki/Electronic_band_structure “Modeling the potential of a crystal as a periodic function with the Born–von Karman boundary condition and plugging in Schrödinger’s equation results in a proof of Bloch’s theorem, which is particularly important in understanding the band structure of crystals.”

Ok, so the “Born–von Karman boundary condition” is helpful in understanding the center area of the brownie. It’s homogenous which is why you can assume the “band index” is periodic / regular and countable. It has to be infinite to work. So, no edges. No edges to the brownie. As I’m interested in the edges, I know where not to look and where something I’m looking at is in the center of the brownie.
 
There’s some important assumptions.
https://en.wikipedia.org/wiki/Electronic_band_structure
 
“Modeling the potential of a crystal as a periodic function with the Born–von Karman boundary condition and plugging in Schrödinger’s equation results in a proof of Bloch’s theorem, which is particularly important in understanding the band structure of crystals.”

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