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Rosa added At_the_band_center_the__.tex
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At the band center the DOS is constant: $\rho_0=1/\pi t$. There is an alternative expression for the chain DOS by
defining $\cos\phi=\frac{\omega-\epsilon_0}{2t}$. Then
\begin{equation}
g^r_{ch}(\omega)=\frac{1}{t}\left(\cos\phi-i\sin\phi\right)=\exp{-i\phi}{t}
\end{equation}
In general we get
\begin{equation}
G^{r}_{n1}=\exp{-i\phi}{t}
\end{equation}
\subsection{Impurity coupled to the semi-infinite chain}
Now we consider that the $0$ state is coupled to the semi-infinite chain with $V$ as the tunneling amplitude
