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Commit c81cc2ae authored by YellowCherry's avatar YellowCherry
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typo - added differential dx

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......@@ -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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