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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 @@ $$ \langle \phi_n | H | \phi_{n+2}\rangle \equiv -t' ≠ 0.$$ ...@@ -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. 1. Write down the new Schrödinger equation for this system.
??? hint ??? hint "hint"
There are now two more terms in the equation: $-t' \phi_{n-2} - t' \phi_{n+2}$. 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 $E(k)$. 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) $. 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: $$C = \frac{\partial U}{\partial T} = \int g(\ome ...@@ -75,5 +75,5 @@ For the heat capacity we have: $$C = \frac{\partial U}{\partial T} = \int g(\ome
### Subquestion 1 ### 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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