Further assume that there is one electron per site

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Unformatted text preview: points] Evaluate the matrix element ∞ H kk′ ≡ ˆ ∫ dx ψ ( x ) Hψ ( x ) , * k k′ −∞ And show that if k ≠ k ′ , the matrix element is identically zero. This means that (1) ψ k ( x ) is ˆ an eigenfunction of H and (2) that the matrix element H kk = E ( k ) , the eigenvalue indexed by k . To complete this evaluation, I needed to know that L −1 ∑ xn = n= 0 1− xL . 1− x (This can be proven straightforwardly...
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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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