Consider the orthogonality relation in (9mlj) (j|qn) = eign-qm)Rj Ns j N-1 eitan-ambia j=0 (qm|j)...

 

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Consider the orthogonality relation in Σ(9mlj) (j|qn) = Σeign-qm)Rj Ns j N₁-1 Σ eitan-ambia j=0 Σ(qm|j) (jan) = j thereby proving orthogonality. N₁ Na where qn = n²7, q = n² =n are the discrete wavevectors, N = L/a is the number of sites in the chain and a is the lattice spacing. By substituting R;= ja and treating this expression as a geometric series, show that = = 8nm, (2.145) (−1)(N-1)(n-m) sin[(n — m)] sin[ (n − m)] N₂ - = 8nm, Consider the orthogonality relation in Σ(9mlj) (j|qn) = Σeign-qm)Rj Ns j N₁-1 Σ eitan-ambia j=0 Σ(qm|j) (jan) = j thereby proving orthogonality. N₁ Na where qn = n²7, q = n² =n are the discrete wavevectors, N = L/a is the number of sites in the chain and a is the lattice spacing. By substituting R;= ja and treating this expression as a geometric series, show that = = 8nm, (2.145) (−1)(N-1)(n-m) sin[(n — m)] sin[ (n − m)] N₂ - = 8nm,