diff --git a/src/11_nearly_free_electron_model.md b/src/11_nearly_free_electron_model.md index 8fa427a1f824ec99f614391d70bfec2b1427e15a..d43a11080ef43769e6946d8f7cb858d12fc2e54d 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 $W$: -$$W = \langle \psi_+ | V(x) | \psi_- \rangle = \frac{1}{a}\int_0^{a} dx \left[e^{-i\pi x/a}\right]^* V(x) \left[e^{i\pi x/a}\right] = \frac{1}{a}\int_0^a e^{-2\pi i x /a} V(x) = V_1$$ +$$W = \langle \psi_+ | V(x) | \psi_- \rangle = \frac{1}{a}\int_0^{a} dx \left[e^{i\pi x/a}\right]^* V(x) \left[e^{-i\pi x/a}\right] = \frac{1}{a}\int_0^a e^{-2\pi i x /a} V(x) = V_1$$ Here $V_1$ is the first Fourier component of $V(x)$ (using a complex Fourier transform).