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). -- GitLab