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-rw-r--r--vorlesungen/punktgruppen/slides.pdfbin32512 -> 36038 bytes
-rw-r--r--vorlesungen/punktgruppen/slides.tex79
2 files changed, 73 insertions, 6 deletions
diff --git a/vorlesungen/punktgruppen/slides.pdf b/vorlesungen/punktgruppen/slides.pdf
index d732296..bd7afc9 100644
--- a/vorlesungen/punktgruppen/slides.pdf
+++ b/vorlesungen/punktgruppen/slides.pdf
Binary files differ
diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
index 380dcec..25761c0 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -7,6 +7,7 @@
% pretty drawings
\usepackage{tikz}
\usetikzlibrary{positioning}
+\usetikzlibrary{arrows.meta}
% Theme
\beamertemplatenavigationsymbolsempty
@@ -64,17 +65,82 @@
\section{Einleitung}
\frame{
- \[
- \psi
- \]
+ \begin{itemize}
+ \item Was heisst \emph{Symmetrie} in der Mathematik?
+ \item Wie kann ein Kristall modelliert werden?
+ \item Aus der Physik: Piezoelektrizit\"at
+ \end{itemize}
+ \begin{center}
+ \begin{tikzpicture}
+ \begin{scope}[
+ node distance = 0cm
+ ]
+ \node[
+ rectangle, fill = gray!40!background,
+ minimum width = 3cm, minimum height = 2cm,
+ ] (body) {\(\vec{E}_p = \vec{0}\)};
+
+ \node[
+ draw, rectangle, thick, white, fill = red!50,
+ minimum width = 3cm, minimum height = 1mm,
+ above = of body
+ ] (pos) {};
+
+ \node[
+ draw, rectangle, thick, white, fill = blue!50,
+ minimum width = 3cm, minimum height = 1mm,
+ below = of body
+ ] (neg) {};
+
+ \draw[white, very thick, -Circle] (pos.east) to ++ (1,0) node (p) {};
+ \draw[white, very thick, -Circle] (neg.east) to ++ (1,0) node (n) {};
+
+ \draw[white, thick, ->] (p) to[out = -80, in = 80] node[midway, right] {\(U = 0\)} (n);
+ \end{scope}
+ \begin{scope}[
+ node distance = 0cm,
+ xshift = 7cm
+ ]
+ \node[
+ rectangle, fill = gray!40!background,
+ minimum width = 3cm, minimum height = 1.5cm,
+ ] (body) {\(\vec{E}_p = \vec{0}\)};
+
+ \node[
+ draw, rectangle, thick, white, fill = red!50,
+ minimum width = 3cm, minimum height = 1mm,
+ above = of body
+ ] (pos) {};
+
+ \node[
+ draw, rectangle, thick, white, fill = blue!50,
+ minimum width = 3cm, minimum height = 1mm,
+ below = of body
+ ] (neg) {};
+
+ \draw[orange, very thick, <-] (pos.north) to node[near end, right] {\(\vec{F}\)} ++(0,1);
+ \draw[orange, very thick, <-] (neg.south) to node[near end, right] {\(\vec{F}\)} ++(0,-1);
+
+ \draw[white, very thick, -Circle] (pos.east) to ++ (1,0) node (p) {};
+ \draw[white, very thick, -Circle] (neg.east) to ++ (1,0) node (n) {};
+
+ \draw[white, thick, ->] (p) to[out = -80, in = 80] node[midway, right] {\(U \neq 0\)} (n);
+ \end{scope}
+ \end{tikzpicture}
+ \end{center}
}
-\section{Geometrische Symmetrien}
+\section{2D Symmetrien}
%% Made in video
\section{Algebraische Symmetrien}
%% Made in video
+\section{3D Symmetrien}
+%% Made in video
+
+\section{Matrizen}
+
\section{Kristalle}
\section{Anwendungen}
@@ -201,6 +267,7 @@
\end{frame}
\frame{
+ \frametitle{Licht in Kristallen}
\begin{columns}[T]
\begin{column}{.5\textwidth}
Symmetriegruppe und Darstellung
@@ -226,10 +293,10 @@
\]
Anisotropisch Dielektrikum
\[
- \ten{R}\ten{\varepsilon}\vec{E} = \frac{\omega^2}{\mu k^2} \vec{E}
+ (\ten{K}\ten{\varepsilon})\vec{E} = \frac{\omega^2}{\mu k^2} \vec{E}
\]
\[
- \vec{E} \in U_\lambda \implies (\ten{R}\ten{\varepsilon}) \vec{E} = \lambda \vec{E}
+ \vec{E} \in U_\lambda \implies (\ten{K}\ten{\varepsilon}) \vec{E} = \lambda \vec{E}
\]
\"Ahenlich auch in der Mechanik
\[