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- TL;DR Summary
- N level (~continuous) energy bands formed from the discrete energy levels of individual atoms when joined in macroscopic lattices of N atoms (N being one jillion)

According to this Wikipedia entry:

https://en.wikipedia.org/wiki/Electronic_band_structure

the discrete energy levels of an isolated atom split into N levels in a macroscopic crystalline lattice (N being the number of atoms in the lattice) forming essentially continuous bands from the discrete levels. I can understand why a molecular bond between two atoms could cause a discrete level to split into two hybrid levels. But I don't understand how a macroscopic lattice could split into N levels (N being enormous), as though ALL of the atoms of the macroscopic material were somehow bonded individually no matter how many intervening atoms. Can someone enlighten me?

https://en.wikipedia.org/wiki/Electronic_band_structure

the discrete energy levels of an isolated atom split into N levels in a macroscopic crystalline lattice (N being the number of atoms in the lattice) forming essentially continuous bands from the discrete levels. I can understand why a molecular bond between two atoms could cause a discrete level to split into two hybrid levels. But I don't understand how a macroscopic lattice could split into N levels (N being enormous), as though ALL of the atoms of the macroscopic material were somehow bonded individually no matter how many intervening atoms. Can someone enlighten me?