deletions | additions       diff --git a/section_Density_of_states_In__.tex b/section_Density_of_states_In__.tex  index 1005ec2..4805662 100644  --- a/section_Density_of_states_In__.tex  +++ b/section_Density_of_states_In__.tex 
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  We first compute the solution to the time-independent Schrödinger equation for a semi-infinte chain. Our results should coincide with the previous in this report. Let us assume a quite general solution for $\mathcal{H}_W$:  \begin{equation}  |\Psi\rangle = \sum_{i=1}^\{i=\infty} \sum_{i=1}^{i=\infty}  c_{i} |i> |i\rangle  \end{equation}  Then   \begin{equation} 
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\end{equation}  or  \begin{equation}  H_{W} \left(\sum_{i=1}^\{i=\infty} \left(\sum_{i=1}^{i=\infty}  c_{i} |i>\right) =E \left(\sum_{i=1}^\{i=\infty} c_{i} |i>\right) \end{equation}  We project onto a state $|m>$ and use the fact that $\langle m | j\rangle=\delta_{m,j}$, the states are an orthornormal basis. Then, we obtain the following   \begin{equation} 
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