diff --git a/docs/8_many_atoms_solutions.md b/docs/8_many_atoms_solutions.md index 9ff34cfcc1a41c562d032947cb3fcb85c7920315..104779219eef36e5b833cdc084989fb5b4ec5b7e 100644 --- a/docs/8_many_atoms_solutions.md +++ b/docs/8_many_atoms_solutions.md @@ -73,8 +73,8 @@ The band gap is $\Delta\omega = \omega_+-\omega_-$ ### Exercise 2: Analyzing the LCAO chain with alternating hoppings 1. The unit cell contains exactly two atoms. By looking at the figure, we can immediately write down the Schrodinger equation relating the probability amplitudes of the atomic orbitals: -$$ E \phi_n = \varepsilon_0 \phi_n - t_1 \psi_n - t_2 \psi_{n-1} $$ -$$ E \psi_n = \varepsilon_0 \psi_n - t_1 \phi_n - t_2 \phi_{n+1} $$ +$$ E \phi_n = \varepsilon_0 \phi_n + t_1 \psi_n + t_2 \psi_{n-1} $$ +$$ E \psi_n = \varepsilon_0 \psi_n + t_1 \phi_n + t_2 \phi_{n+1} $$ 2. This follows directly from substituting the Ansatz