X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=physics_compact%2Fsolid.tex;h=e19b7cef4823afd4f95daf2d2fdc34b7f7df73a3;hp=0d5b1b2d0d6cdee705b7002bbf76a4b0c74f4e73;hb=eac23ae428984d20c62851681234b206ec1e3dc7;hpb=147329059cdda2ebf293426b7fdbcd13b0c783f9

diff --git a/physics_compact/solid.tex b/physics_compact/solid.tex
index 0d5b1b2..e19b7ce 100644
--- a/physics_compact/solid.tex
+++ b/physics_compact/solid.tex
@@ -109,3 +109,44 @@ E_1 + E_2 < E_2 + E_1 +
 is revealed, which proofs the Hohenberg Kohn theorem.% \qed
 \end{proof}
 
+\section{Electron-ion interaction}
+
+\subsection{Pseudopotential theory}
+
+The basic idea of pseudopotential theory is to only describe the valence electrons, which are responsible for the chemical bonding as well as the electronic properties for the most part.
+
+\subsubsection{Orthogonalized planewave method}
+
+Due to the orthogonality of the core and valence wavefunctions, the latter exhibit strong oscillations within the core region of the atom.
+This requires a large amount of planewaves $\ket{k}$ to adequatley model the valence electrons.
+
+In a very general approach, the orthogonalized planewave (OPW) method introduces a new basis set
+\begin{equation}
+\ket{k}_{\text{OPW}} = \ket{k} - \sum_t \ket{t}\bra{t}k\rangle \text{ ,}
+\end{equation} 
+with $\ket{t}$ being the eigenstates of the core electrons.
+The new basis is orthogonal to the core states $\ket{t}$.
+\begin{equation}
+\braket{t}{k}_{\text{OPW}} =
+\braket{t}{k} - \sum_{t'} \braket{t}{t'}\braket{t'}{k} =
+\braket{t}{k} - \braket{t}{k}=0
+\end{equation}
+The number of planewaves required for reasonably converged electronic structure calculations is tremendously reduced by utilizing the OPW basis set.
+
+\subsubsection{Pseudopotential method}
+
+\subsubsection{Norm conserving pseudopotentials}
+
+\begin{equation}
+V=\ket{lm}V_l(r)\bra{lm}
+\end{equation}
+
+\subsubsection{Fully separable form of the pseudopotential}
+
+\subsection{Spin orbit interaction}
+
+
+\subsubsection{Perturbative treatment}
+
+\subsubsection{Non-perturbative method}
+