Electron-phonon interactions and Kohn anomalies

Electron-phonon interactions

Derivation of Hamiltonian Electron-Phonon Coupling

The Hamiltonian for the electron-phonon interaction can be described as
\begin{equation}\label{reio}

$H=H_{el}^{0}+H_{ph}^{0}+H_{coul}+H_{int}$
\end{equation}

Where $H_{el}^{0}=$

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