From f17c5a78684c5a01c3145a319faec4eded690891 Mon Sep 17 00:00:00 2001
From: Anton Akhmerov <anton.akhmerov@gmail.com>
Date: Mon, 15 Apr 2024 10:06:00 +0200
Subject: [PATCH] fix hopping sign in 8.2.2 solutions

---
 docs/8_many_atoms_solutions.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/docs/8_many_atoms_solutions.md b/docs/8_many_atoms_solutions.md
index 9ff34cf..1047792 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
 
-- 
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