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pkirwin 2021-04-01 16:09:48 -06:00
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@ -311,7 +311,7 @@ S_u = [1, s; s, 1];
\item %2cvii \item %2cvii
Since \(e^{2\pi n} = 1\), we have: Since \(e^{2\pi n} = 1\), we have:
\begin{align*} \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). \phi_n(k+\frac{2\pi}{a}) &= \phi_n(k).
\end{align*} \end{align*}
Therefore wavefunctions for which \(k\) is separated by \(\frac{2\pi}{a}\) are equivalent, and we Therefore wavefunctions for which \(k\) is separated by \(\frac{2\pi}{a}\) are equivalent, and we