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Why do we need a finite system to find the find the wave function and a infinite system to find the band structure?

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  • $\begingroup$ You can find the wave function in both cases. The band structure has to do with the energy structure, not with the eigenfunctions. Maybe if you elaborate what you mean, possibly quoting the source of confusion, we could help you better $\endgroup$ – glS Jan 22 '15 at 13:51
  • $\begingroup$ No, we don't need. We can find the wavefunction for infinite system and we can find the band structure (with discrete Brillouin zone) for finite crystal (using Born-von Karmann boundary conditions). $\endgroup$ – Ruslan Jan 22 '15 at 13:51
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You don't-- but unless you want to deal with the surfaces of the crystal, which don't usually have a major affect on the bulk macroscopic properties of the crystal, one usually uses periodic boundary conditions.

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