diff --git a/src/7_tight_binding.md b/src/7_tight_binding.md index dff34807a3c8d005625ed4251c95cebcb4f55943..b4d1b5bd3388e3cb2cdd3de96e2a818fd823441e 100644 --- a/src/7_tight_binding.md +++ b/src/7_tight_binding.md @@ -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) $. diff --git a/src/7_tight_binding_model_sol.md b/src/7_tight_binding_model_sol.md index 3e349c77f8fd44d054174b9f337055199a4c4298..37a9e415eec4b325115c780a27f41d6bb727218c 100644 --- a/src/7_tight_binding_model_sol.md +++ b/src/7_tight_binding_model_sol.md @@ -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}$$.