diff --git a/PS3/doc.pdf b/PS3/doc.pdf
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Binary files a/PS3/doc.pdf and b/PS3/doc.pdf differ
diff --git a/PS3/doc.tex b/PS3/doc.tex
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--- a/PS3/doc.tex
+++ b/PS3/doc.tex
@@ -311,7 +311,7 @@ S_u = [1, s; s, 1];
                 \item %2cvii
                 Since \(e^{2\pi n} = 1\), we have:
                 \begin{align*}
-                    \phi_n(k+\frac{2\pi}{a}) &= Ce^{i(k+\frac{2\pi}{a} \cdot nA} = Ce^{i(k \cdot nA} \\
+                    \phi_n(k+\frac{2\pi}{a}) &= Ce^{i(k+\frac{2\pi}{a}) \cdot nA} = Ce^{ik \cdot nA} \\
                     \phi_n(k+\frac{2\pi}{a}) &= \phi_n(k).
                 \end{align*}
                 Therefore wavefunctions for which \(k\) is separated by \(\frac{2\pi}{a}\) are equivalent, and we