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Commit 53888703 authored by Lars kleyn Winkel's avatar Lars kleyn Winkel
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Update src/7_tight_binding_model_sol.md, src/7_tight_binding.md files

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......@@ -284,13 +284,13 @@ $$ \langle \phi_n | H | \phi_{n+2}\rangle \equiv -t' ≠ 0.$$
1. Write down the new Schrödinger equation for this system.
??? hint
??? hint "hint"
There are now two more terms in the equation: $-t' \phi_{n-2} - t' \phi_{n+2}$.
2. Solve the Schrödinger equation to find the dispersion relation $E(k)$.
??? hint
??? hint "hint"
Use the same Ansatz as for the nearest neighbors case: $ \phi_n = \phi_0 \exp(ikna) $.
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......@@ -75,5 +75,5 @@ For the heat capacity we have: $$C = \frac{\partial U}{\partial T} = \int g(\ome
### Subquestion 1
The Schrödinger equation is given as: $E|\phi_n> = \sum_m \hat H|\phi_m>$ such that we find $$ E\phi_n = E_0\phi_n -t\phi_{n-1} -t\phi_{n+1} -t'\phi_{n-2} -t'\phi_{n+2}$$.
The Schrödinger equation is given as: $E|\phi_n> = \sum_m \hat H|\phi_m>$ such that we find $$ E\phi_n = E_0\phi_n - t\phi_{n-1} - t\phi_{n+1} - t'\phi_{n-2} - t'\phi_{n+2}$$.
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