K x 1 l 1 exp i k au u x l u0 note

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Unformatted text preview: dition to Bloch’s theorem, the periodic boundary conditions imply that the eigenfunctions must also obey: ψ k ( x ) = ψ k ( x + L a ) with a the distance between nearest neighbor atoms in the chain. [15 points] Noting that Bloch’s theorem implies that we can write ψ k ( x ) = exp [ i k x ]U k ( x ) , with U k ( x ) = U k ( x + j a ) ∀j ∈ Integers , prove that k is of the form. k= 2...
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