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I was reading Physics SE 228313. It talks about using Born-von Karman condition to model metal lattices.

Is there any mathematical justification that approximations to physical condition would give well-approximated solutions to physical problems? Putting aside mathematical rigor, it is not even physically intuitive for me that it holds as, e.g. additional periodic conditions may lead to coherence and interference.

Note: This question applies to bulk effects only.

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