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

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

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Transcribed Image Text:

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,

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