To complete this evaluation i needed to know that l 1

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Unformatted text preview: π n, n = 0,1, 2, 3, ..., L − 1 . La Defining ϕ u ( x ) = ϕ u − L ( x ) show that the state below [15 points] is properly normalized, and [20 points] satisfies Bloch’s theorem. ψ k ( x) = 1 L −1 ∑ exp [i k au ]ϕ u ( x ) . L u=0 Note that there are L possible values of k. We can use the states ψ k ( x ) to construct the Hamiltonian matrix, which is, in principle, L × L . [20...
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This homework help was uploaded on 02/17/2014 for the course PHYSICS 214 taught by Professor A during the Spring '10 term at University of Illinois, Urbana Champaign.

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