From c81cc2ae626a74a0ee3195c108e768ecda2f0d83 Mon Sep 17 00:00:00 2001
From: YellowCherry <giandebruin@hotmail.com>
Date: Mon, 8 Apr 2019 21:25:57 +0000
Subject: [PATCH] typo - added differential dx

---
 src/11_nearly_free_electron_model.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/11_nearly_free_electron_model.md b/src/11_nearly_free_electron_model.md
index d43a1108..06decabe 100644
--- a/src/11_nearly_free_electron_model.md
+++ b/src/11_nearly_free_electron_model.md
@@ -108,7 +108,7 @@ Check out section 15.1.1 of the book for the details of this calculation.
 
 Now we expand the definition of $W$:
 
-$$W = \langle \psi_+ | V(x) | \psi_- \rangle = \frac{1}{a}\int_0^{a} dx \left[e^{i\pi x/a}\right]^* V(x) \left[e^{-i\pi x/a}\right] = \frac{1}{a}\int_0^a e^{-2\pi i x /a} V(x) = V_1$$
+$$W = \langle \psi_+ | V(x) | \psi_- \rangle = \frac{1}{a}\int_0^{a} dx \left[e^{i\pi x/a}\right]^* V(x) \left[e^{-i\pi x/a}\right] = \frac{1}{a}\int_0^a e^{-2\pi i x /a} V(x) dx = V_1$$
 
 Here $V_1$ is the first Fourier component of $V(x)$ (using a complex Fourier transform).
 
-- 
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