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For 1D linear chain, a is the lattice constant, u is the displacement of every atom from the equilibrium. N is the total number of atom

the boundary condition is u(0)=u(Na)

but my question is why? why are they equal. why does the atom at one end of the chain have to perform the same as the atom at the other end?

Sometimes, I see that sb. writes boundary condition as u(na)=u(na+Na). If there is only N atoms, how could there be u(na+Na)?

Thanks

stalk
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1 Answers1

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They don't, but this is the importance of understanding boundary conditions. Are there periodic boundary conditions? From the last statement, u(na)=u(na+Na), it sounds like there are. It does not mean that there are more than N atoms. It means that once you go past the last one at N, you hop back around to the first one. The 0th and Nth atom are equivalent.

daFireman
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  • then, why does the u(oth) equal to the u(Nth) ? u is the displacement of atom from its equilibrium. So why does the displacement of the 0th atom equal to the displacement of the Nth atom? – stalk Oct 03 '17 at 04:50