From 4b3f4be3305d130c0435c269fd038eb049252f5d Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Wed, 28 Apr 2021 21:52:38 +0200
Subject: Create slides

---
 vorlesungen/punktgruppen/slides.tex | 61 +++++++++++++++++++++++++++++++++++++
 1 file changed, 61 insertions(+)
 create mode 100644 vorlesungen/punktgruppen/slides.tex

(limited to 'vorlesungen/punktgruppen/slides.tex')

diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
new file mode 100644
index 0000000..5c6982c
--- /dev/null
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -0,0 +1,61 @@
+\documentclass[12pt, xcolor, aspectratio=169]{beamer}
+
+
+% Theme
+\beamertemplatenavigationsymbolsempty
+
+% set look
+\usetheme{default} 
+\usecolortheme{fly}
+
+%% Set font
+\usepackage[p,osf]{scholax}
+\usepackage{amsmath}
+\usepackage[scaled=1.075,ncf,vvarbb]{newtxmath}
+
+% set colors
+\definecolor{background}{HTML}{202020}
+
+\setbeamercolor{normal text}{fg=white, bg=background}
+\setbeamercolor{structure}{fg=white}
+
+\setbeamercolor{item projected}{use=item,fg=background,bg=item.fg!35}
+
+\setbeamercolor*{palette primary}{use=structure,fg=white,bg=structure.fg}
+\setbeamercolor*{palette secondary}{use=structure,fg=white,bg=structure.fg!75}
+\setbeamercolor*{palette tertiary}{use=structure,fg=white,bg=structure.fg!50}
+\setbeamercolor*{palette quaternary}{fg=white,bg=background}
+
+\setbeamercolor*{block title}{parent=structure}
+\setbeamercolor*{block body}{fg=background, bg=}
+
+\setbeamercolor*{framesubtitle}{fg=white}
+
+% Metadata
+\title{\LARGE \scshape Punktgruppen und Kristallen}
+\author[N. Pross, T. T\"onz]{Naoki Pross, Tim T\"onz}
+\institute{Hochschule f\"ur Technik OST, Rapperswil}
+\date{10. Mai 2021}
+
+% Slides
+\begin{document}
+\begin{frame}{}
+\titlepage
+\end{frame}
+
+% \begin{frame}{}
+% \tableofcontents
+% \end{frame}
+
+\section{Einleitung}
+\begin{frame}{Kristallen}
+\[
+  \psi
+\]
+\end{frame}
+
+\section{Geometrische Symmetrien}
+\section{Algebraische Symmetrien}
+\section{Kristallen}
+
+\end{document}
-- 
cgit v1.2.1


From 152b7c463b1ae7cd7916dff075a11b306e5c22fc Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Sat, 1 May 2021 19:43:15 +0200
Subject: Add section title pages

---
 vorlesungen/punktgruppen/slides.tex | 20 ++++++++++++++++++++
 1 file changed, 20 insertions(+)

(limited to 'vorlesungen/punktgruppen/slides.tex')

diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
index 5c6982c..8394451 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -1,5 +1,8 @@
 \documentclass[12pt, xcolor, aspectratio=169]{beamer}
 
+% language
+\usepackage{polyglossia}
+\setmainlanguage{german}
 
 % Theme
 \beamertemplatenavigationsymbolsempty
@@ -31,6 +34,15 @@
 
 \setbeamercolor*{framesubtitle}{fg=white}
 
+\setbeamertemplate{section page}
+{
+  \begin{center}
+    \Huge
+    \insertsection
+  \end{center}
+}
+\AtBeginSection{\frame{\sectionpage}}
+
 % Metadata
 \title{\LARGE \scshape Punktgruppen und Kristallen}
 \author[N. Pross, T. T\"onz]{Naoki Pross, Tim T\"onz}
@@ -55,7 +67,15 @@
 \end{frame}
 
 \section{Geometrische Symmetrien}
+%% Made in video
+
 \section{Algebraische Symmetrien}
+\begin{frame}{}
+  Hello
+\end{frame}
+
 \section{Kristallen}
 
+\section{Anwendungen}
+
 \end{document}
-- 
cgit v1.2.1


From 6e507ac59576c7b7ac5f0c80eee4e3a36b599a7e Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Sat, 1 May 2021 21:09:26 +0200
Subject: Add slide for 4th roots of 1

---
 vorlesungen/punktgruppen/slides.tex | 73 +++++++++++++++++++++++++++++--------
 1 file changed, 58 insertions(+), 15 deletions(-)

(limited to 'vorlesungen/punktgruppen/slides.tex')

diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
index 8394451..2199b26 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -10,6 +10,7 @@
 % set look
 \usetheme{default} 
 \usecolortheme{fly}
+\usefonttheme{serif}
 
 %% Set font
 \usepackage[p,osf]{scholax}
@@ -51,28 +52,70 @@
 
 % Slides
 \begin{document}
-\begin{frame}{}
-\titlepage
-\end{frame}
-
-% \begin{frame}{}
-% \tableofcontents
-% \end{frame}
+\frame{\titlepage}
+\frame{\tableofcontents}
 
 \section{Einleitung}
-\begin{frame}{Kristallen}
-\[
-  \psi
-\]
-\end{frame}
+\frame{
+  \[
+    \psi
+  \]
+}
 
 \section{Geometrische Symmetrien}
 %% Made in video
 
 \section{Algebraische Symmetrien}
-\begin{frame}{}
-  Hello
-\end{frame}
+\frame{
+  \begin{columns}
+    \begin{column}{.3\textwidth}
+      Produkt mit \(i\)
+      \begin{align*}
+        1 \cdot i &= i \\
+        i \cdot i &= -1 \\
+        -1 \cdot i &= -i \\
+        -i \cdot i &= 1
+      \end{align*}
+      \pause
+      %
+      Gruppe
+      \begin{align*}
+        G &= \left\{
+          1, i, -1, -i
+        \right\} \\
+        &= \left\{
+          1, i, i^2, i^3
+        \right\} \\
+        Z_4 &= \left\{
+          \mathbb{1}, r, r^2, r^3
+        \right\}
+      \end{align*}
+      \pause
+      %
+    \end{column}
+    \begin{column}{.5\textwidth}
+      %
+      Darstellung
+      \[
+        \phi : Z_4 \to G
+      \]
+      \begin{align*}
+        \phi(\mathbb{1}) &= 1 & \phi(r^2) &= i^2 \\
+        \phi(r) &= i & \phi(r^3) &= i^3
+      \end{align*}
+      \pause
+      %
+      Homomorphismus
+      \begin{align*}
+        \phi(r \circ \mathbb{1}) &= \phi(r) \cdot \phi(\mathbb{1}) \\
+        &= i \cdot 1
+      \end{align*}
+      \pause
+      %
+      \(\phi\) ist bijektiv \(\implies Z_4 \cong G\)
+    \end{column}
+  \end{columns}
+}
 
 \section{Kristallen}
 
-- 
cgit v1.2.1


From 6eed506199b5ff21b58af9f8db6477d5af56aa0b Mon Sep 17 00:00:00 2001
From: tim30b <tim.toenz@ost.ch>
Date: Mon, 3 May 2021 18:45:24 +0200
Subject: Write Intro

---
 vorlesungen/punktgruppen/slides.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

(limited to 'vorlesungen/punktgruppen/slides.tex')

diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
index 2199b26..1c1b1d8 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -45,7 +45,7 @@
 \AtBeginSection{\frame{\sectionpage}}
 
 % Metadata
-\title{\LARGE \scshape Punktgruppen und Kristallen}
+\title{\LARGE \scshape Punktgruppen und Kristalle}
 \author[N. Pross, T. T\"onz]{Naoki Pross, Tim T\"onz}
 \institute{Hochschule f\"ur Technik OST, Rapperswil}
 \date{10. Mai 2021}
@@ -117,7 +117,7 @@
   \end{columns}
 }
 
-\section{Kristallen}
+\section{Kristalle}
 
 \section{Anwendungen}
 
-- 
cgit v1.2.1


From 2de3a8ffcfb661abfde05cf3611ad08d5a1160fc Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Tue, 4 May 2021 20:08:33 +0200
Subject: Create slides for applications

---
 vorlesungen/punktgruppen/slides.tex | 202 ++++++++++++++++++++++++++++--------
 1 file changed, 160 insertions(+), 42 deletions(-)

(limited to 'vorlesungen/punktgruppen/slides.tex')

diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
index 1c1b1d8..380dcec 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -4,6 +4,10 @@
 \usepackage{polyglossia}
 \setmainlanguage{german}
 
+% pretty drawings
+\usepackage{tikz}
+\usetikzlibrary{positioning}
+
 % Theme
 \beamertemplatenavigationsymbolsempty
 
@@ -44,6 +48,9 @@
 }
 \AtBeginSection{\frame{\sectionpage}}
 
+% Macros
+\newcommand{\ten}[1]{#1}
+
 % Metadata
 \title{\LARGE \scshape Punktgruppen und Kristalle}
 \author[N. Pross, T. T\"onz]{Naoki Pross, Tim T\"onz}
@@ -66,59 +73,170 @@
 %% Made in video
 
 \section{Algebraische Symmetrien}
+%% Made in video
+
+\section{Kristalle}
+
+\section{Anwendungen}
+\begin{frame}[fragile]{}
+  \centering
+  \begin{tikzpicture}[
+      box/.style = {
+        rectangle, thick, draw = white, fill = darkgray!50!background,
+        minimum height = 1cm, outer sep = 2mm,
+      },
+    ]
+
+    \matrix [nodes = {box, align = center}, column sep = 1cm, row sep = 1.5cm] {
+      & \node (A) {32 Punktgruppe}; \\
+      \node (B) {11 Mit\\ Inversionszentrum}; & \node (C) {21 Ohne\\ Inversionszentrum}; \\
+      & \node[fill=red!20!background] (D) {20 Piezoelektrisch}; & \node (E) {1 Nicht\\ piezoelektrisch}; \\
+    };
+
+    \draw[thick, ->] (A.west) to[out=180, in=90] (B.north);
+    \draw[thick, ->] (A.south) to (C);
+    \draw[thick, ->] (C.south) to (D.north);
+    \draw[thick, ->] (C.east) to[out=0, in=90] (E.north);
+  \end{tikzpicture}
+\end{frame}
+
+\begin{frame}[fragile]{}
+  \begin{tikzpicture}[
+      overlay, xshift = 1.5cm, yshift = 1.5cm,
+      node distance = 2mm,
+      charge/.style = {
+        circle, draw = white, thick,
+        minimum size = 5mm
+      },
+      positive/.style = { fill = red!50 },
+      negative/.style = { fill = blue!50 },
+    ]
+
+    \node[font = {\large\bfseries}, align = center] (title) at (6,0) {Mit und Ohne\\ Symmetriezentrum};
+    \node[below = of title] {Polarisation Feld \(\vec{E}_p\)};
+
+    \begin{scope}
+      \matrix[nodes = { charge }, row sep = 8mm, column sep = 8mm] {
+        \node[positive] {}; & \node[negative] (N) {}; & \node [positive] {}; \\
+        \node[negative] (W) {}; & \node[positive] {}; & \node [negative] (E) {}; \\
+        \node[positive] {}; & \node[negative] (S) {}; & \node [positive] {}; \\
+      };
+      \draw[gray, dashed] (W) to (N) to (E) to (S) to (W);
+    \end{scope}
+
+    \begin{scope}[yshift=-4.5cm]
+      \matrix[nodes = { charge }, row sep = 5mm, column sep = 1cm] {
+        \node[positive] (NW) {}; & \node[negative] (N) {}; & \node [positive] (NE) {}; \\
+        \node[negative] (W) {}; & \node[positive] {}; & \node [negative] (E) {}; \\
+        \node[positive] (SW) {}; & \node[negative] (S) {}; & \node [positive] (SE) {}; \\
+      };
+
+      \foreach \d in {NW, N, NE} {
+        \draw[orange, very thick, <-] (\d) to ++(0,.7);
+      }
+
+      \foreach \d in {SW, S, SE} {
+        \draw[orange, very thick, <-] (\d) to ++(0,-.7);
+      }
+
+      \draw[gray, dashed] (W) to (N) to (E) to (S) to (W);
+    \end{scope}
+
+    \begin{scope}[xshift=11cm]
+      \foreach \x/\t [count=\i] in {60/positive, 120/negative, 180/positive, 240/negative, 300/positive, 360/negative} {
+        \node[charge, \t] (C\i) at (\x:1.5cm) {};
+      }
+
+      \draw[white] (C1) to (C2) to (C3) to (C4) to (C5) to (C6) to (C1);
+      \draw[gray, dashed] (C2) to (C4) to (C6) to (C2);
+    \end{scope}
+
+    \begin{scope}[xshift=6cm, yshift=-4.5cm]
+      \node[charge, positive, yshift=-2.5mm] (C1) at ( 60:1.5cm) {};
+      \node[charge, negative, yshift=-2.5mm] (C2) at (120:1.5cm) {};
+      \node[charge, positive, xshift=-2.5mm] (C3) at (180:1.5cm) {};
+      \node[charge, negative, yshift= 2.5mm] (C4) at (240:1.5cm) {};
+      \node[charge, positive, yshift= 2.5mm] (C5) at (300:1.5cm) {};
+      \node[charge, negative, xshift= 2.5mm] (C6) at (360:1.5cm) {};
+
+      \draw[white] (C1) to (C2) to (C3) to (C4) to (C5) to (C6) to (C1);
+      % \draw[gray, dashed] (C2) to (C4) to (C6) to (C2);
+
+      \foreach \d in {C1, C2} {
+        \draw[orange, very thick, <-] (\d) to ++(0,.7);
+      }
+
+      \foreach \d in {C4, C5} {
+        \draw[orange, very thick, <-] (\d) to ++(0,-.7);
+      }
+
+      \node[white] (E) {\(\vec{E}_p\)};
+      \begin{scope}[node distance = .5mm]
+        \node[blue!50, right = of E] {\(-\)};
+        \node[red!50, left = of E] {\(+\)};
+      \end{scope}
+    \end{scope}
+
+    \begin{scope}[xshift=11cm, yshift=-4.5cm]
+      \node[charge, positive, yshift= 2.5mm] (C1) at ( 60:1.5cm) {};
+      \node[charge, negative, yshift= 2.5mm] (C2) at (120:1.5cm) {};
+      \node[charge, positive, xshift= 2.5mm] (C3) at (180:1.5cm) {};
+      \node[charge, negative, yshift=-2.5mm] (C4) at (240:1.5cm) {};
+      \node[charge, positive, yshift=-2.5mm] (C5) at (300:1.5cm) {};
+      \node[charge, negative, xshift=-2.5mm] (C6) at (360:1.5cm) {};
+
+      \draw[white] (C1) to (C2) to (C3) to (C4) to (C5) to (C6) to (C1);
+      % \draw[gray, dashed] (C2) to (C4) to (C6) to (C2);
+
+      \draw[orange, very thick, <-] (C6) to ++(.7,0);
+      \draw[orange, very thick, <-] (C3) to ++(-.7,0);
+
+      \node[white] (E) {\(\vec{E}_p\)};
+      \begin{scope}[node distance = .5mm]
+        \node[blue!50, right = of E] {\(-\)};
+        \node[red!50, left = of E] {\(+\)};
+      \end{scope}
+    \end{scope}
+  \end{tikzpicture}
+\end{frame}
+
 \frame{
-  \begin{columns}
-    \begin{column}{.3\textwidth}
-      Produkt mit \(i\)
+  \begin{columns}[T]
+    \begin{column}{.5\textwidth}
+      Symmetriegruppe und Darstellung
       \begin{align*}
-        1 \cdot i &= i \\
-        i \cdot i &= -1 \\
-        -1 \cdot i &= -i \\
-        -i \cdot i &= 1
+        G &= \left\{\mathbb{1}, r, \sigma, \dots \right\} \\
+        &\Phi : G \to O(n)
       \end{align*}
-      \pause
-      %
-      Gruppe
       \begin{align*}
-        G &= \left\{
-          1, i, -1, -i
-        \right\} \\
-        &= \left\{
-          1, i, i^2, i^3
-        \right\} \\
-        Z_4 &= \left\{
-          \mathbb{1}, r, r^2, r^3
-        \right\}
+        U_\lambda &= \left\{ v : \Phi v = \lambda v \right\} \\
+        &= \mathrm{null}\left(\Phi - \lambda I\right)
       \end{align*}
-      \pause
-      %
+      Helmholtz Wellengleichung
+      \[
+        \nabla^2 \vec{E} = \ten{\varepsilon}\mu
+        \frac{\partial^2}{\partial t^2} \vec{E}
+      \]
     \end{column}
     \begin{column}{.5\textwidth}
-      %
-      Darstellung
+      Ebene Welle
       \[
-        \phi : Z_4 \to G
+        \vec{E} = \vec{E}_0 \exp\left[i
+          \left(\vec{k}\cdot\vec{r} - \omega t \right)\right]
+      \]
+      Anisotropisch Dielektrikum
+      \[
+        \ten{R}\ten{\varepsilon}\vec{E} = \frac{\omega^2}{\mu k^2} \vec{E}
+      \]
+      \[
+        \vec{E} \in U_\lambda \implies (\ten{R}\ten{\varepsilon}) \vec{E} = \lambda \vec{E}
+      \]
+      \"Ahenlich auch in der Mechanik
+      \[
+        \vec{F} = \kappa \vec{x} \quad \text{(Hooke)}
       \]
-      \begin{align*}
-        \phi(\mathbb{1}) &= 1 & \phi(r^2) &= i^2 \\
-        \phi(r) &= i & \phi(r^3) &= i^3
-      \end{align*}
-      \pause
-      %
-      Homomorphismus
-      \begin{align*}
-        \phi(r \circ \mathbb{1}) &= \phi(r) \cdot \phi(\mathbb{1}) \\
-        &= i \cdot 1
-      \end{align*}
-      \pause
-      %
-      \(\phi\) ist bijektiv \(\implies Z_4 \cong G\)
     \end{column}
   \end{columns}
 }
 
-\section{Kristalle}
-
-\section{Anwendungen}
-
 \end{document}
-- 
cgit v1.2.1


From 5d2f685df7b2d7691625937609cf92be9fc8c9da Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Tue, 4 May 2021 20:36:41 +0200
Subject: Create intro slide

---
 vorlesungen/punktgruppen/slides.tex | 79 ++++++++++++++++++++++++++++++++++---
 1 file changed, 73 insertions(+), 6 deletions(-)

(limited to 'vorlesungen/punktgruppen/slides.tex')

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
       \[
-- 
cgit v1.2.1


From 714f0685c47dfa46775859024936b22f610619c9 Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Wed, 5 May 2021 13:03:09 +0200
Subject: Create crystal slides

---
 vorlesungen/punktgruppen/slides.tex | 115 +++++++++++++++++++++++++++++++++++-
 1 file changed, 112 insertions(+), 3 deletions(-)

(limited to 'vorlesungen/punktgruppen/slides.tex')

diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
index 25761c0..e800a87 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -8,6 +8,7 @@
 \usepackage{tikz}
 \usetikzlibrary{positioning}
 \usetikzlibrary{arrows.meta}
+\usetikzlibrary{calc}
 
 % Theme
 \beamertemplatenavigationsymbolsempty
@@ -95,7 +96,7 @@
         \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);
+        \draw[white, thick, ->] (p) to[out = -70, in = 70] node[midway, right] {\(U = 0\)} (n);
       \end{scope}
       \begin{scope}[
           node distance = 0cm,
@@ -124,7 +125,7 @@
         \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);
+        \draw[white, thick, ->] (p) to[out = -70, in = 70] node[midway, right] {\(U \neq 0\)} (n);
       \end{scope}
     \end{tikzpicture}
   \end{center}
@@ -142,6 +143,114 @@
 \section{Matrizen}
 
 \section{Kristalle}
+\begin{frame}[fragile]{}
+  \begin{columns}[T]
+    \begin{column}{.5\textwidth}
+      Kristallgitter:
+      \(n_i \in \mathbb{Z}\),
+      \(\vec{a}_i \in \mathbb{R}^3\)
+      \[
+        \vec{r} = n_1 \vec{a}_1 + n_2 \vec{a}_2 + n_3 \vec{a}_3
+      \]
+      \begin{center}
+          \begin{tikzpicture}[
+              dot/.style = {
+                draw, circle, thick, white, fill = gray!40!background,
+                minimum size = 2mm,
+                inner sep = 0pt,
+                outer sep = 1mm,
+              },
+            ]
+
+            \begin{scope}
+              \clip (-1,-1) rectangle (4,3);
+              \foreach \y in {-5,-4,...,5} {
+                \foreach \x in {-5,-4,...,5} {
+                  \node[dot, xshift=3mm*\y] (N\x\y) at (\x, \y) {};
+                }
+              }
+            \end{scope}
+
+            \draw[white, thick] (-1, -1) rectangle (4,3);
+
+            \draw[red!80!background, thick, ->] (N00) to node[midway, below] {\(\vec{a}_1\)} (N10);
+            \draw[cyan!80!background, thick, ->] (N00) to node[midway, left] {\(\vec{a}_2\)} (N01);
+
+          \end{tikzpicture}
+      \end{center}
+      Invariant (symmetrisch) unten Translation
+      \[
+        Q_i(\vec{r}) = \vec{r} + \vec{a}_i
+      \]
+    \end{column}
+    \begin{column}{.5\textwidth}
+      Wie kombiniert sich \(Q_i\) mit der anderen Symmetrien?
+      \begin{center}
+        \begin{tikzpicture}[
+            dot/.style = {
+              draw, circle, thick, white, fill = gray!40!background,
+              minimum size = 2mm,
+              inner sep = 0pt,
+              outer sep = 1mm,
+            },
+          ]
+
+          \node[dot] (A1) at (0,0) {};
+          \node[below left] at (A1) {\(A\)};
+
+          \node[dot] (A2) at (2.5,0) {};
+          \node[below right] at (A2) {\(A'\)};
+
+          \draw[red!80!background, thick, ->] 
+            (A1) to node[midway, below] {\(\vec{Q}\)} (A2);
+
+          \node[dot] (B1) at (120:2.5) {};
+          \node[above left] at (B1) {\(B\)};
+
+          \draw[green!70!background, thick, ->]
+            (A1) ++(.5,0) arc (0:120:.5) node[midway, above, xshift=1mm] {\(C_n\)};
+          \draw[red!80!background, dashed, thick, ->] (A1) to (B1);
+
+
+          \node[dot] (B2) at ($(A2)+(60:2.5)$) {};
+          \node[above right] at (B2) {\(B'\)};
+
+          \draw[green!70!background, thick, dashed, ->] (A2) ++(-.5,0) arc (180:60:.5);
+          \draw[red!80!background, dashed, thick, ->] (A2) to (B2);
+
+          \draw[yellow!80!background, thick, ->] (B1) to node[above, midway] {\(\vec{Q}'\)} (B2);
+
+          \draw[gray, dashed, thick] (A1) to (A1 |- B1) node (X) {};
+          \draw[gray, dashed, thick] (A2) to (A2 |- B2);
+
+          \node[above left, xshift=-2mm] at (X) {\(x\)};
+        \end{tikzpicture}
+      \end{center}
+      Sei \(q = |\vec{Q}|\), \(\alpha = 2\pi/n\) und \(n \in \mathbb{N}\)
+      \begin{align*}
+        q' = n q &= q + 2x \\
+        nq &= q + 2q\sin(\alpha - \pi/2) \\
+        n &= 1 - 2\cos\alpha
+      \end{align*}
+    \end{column}
+  \end{columns}
+\end{frame}
+
+\frame{
+  \begin{columns}[T]
+    \begin{column}{.5\textwidth}
+      Somit muss
+      \[
+        \alpha = \cos^{-1}\left(\frac{m-1}{2}\right)
+      \]
+      \begin{gather*}
+        \alpha \in \left\{ 0, 60^\circ, 90^\circ, 120^\circ, 180^\circ \right\}
+      \end{gather*}
+    \end{column}
+    \begin{column}{.5\textwidth}
+    \end{column}
+  \end{columns}
+}
 
 \section{Anwendungen}
 \begin{frame}[fragile]{}
@@ -154,7 +263,7 @@
     ]
 
     \matrix [nodes = {box, align = center}, column sep = 1cm, row sep = 1.5cm] {
-      & \node (A) {32 Punktgruppe}; \\
+      & \node (A) {32 Punktgruppen}; \\
       \node (B) {11 Mit\\ Inversionszentrum}; & \node (C) {21 Ohne\\ Inversionszentrum}; \\
       & \node[fill=red!20!background] (D) {20 Piezoelektrisch}; & \node (E) {1 Nicht\\ piezoelektrisch}; \\
     };
-- 
cgit v1.2.1


From cbcb1b7f273875a0faf6ffa3d4daf7de7d6e0490 Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Wed, 5 May 2021 14:57:07 +0200
Subject: Add slides for matrices

---
 vorlesungen/punktgruppen/slides.tex | 55 +++++++++++++++++++++++++++++++------
 1 file changed, 47 insertions(+), 8 deletions(-)

(limited to 'vorlesungen/punktgruppen/slides.tex')

diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
index e800a87..54798f1 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -141,6 +141,44 @@
 %% Made in video
 
 \section{Matrizen}
+\frame{
+  \begin{columns}[T]
+    \begin{column}{.5\textwidth}
+      Symmetriegruppe
+      \[
+        G = \left\{\mathbb{1}, r, \sigma, \dots \right\}
+      \]
+      Matrixdarstellung
+      \begin{align*}
+        \Phi : G &\to O(3) \\
+        g &\mapsto \Phi_g
+      \end{align*}
+      Orthogonale Gruppe
+      \[
+        O(n) = \left\{ Q \in \mathrm{GL}_n(\mathbb{R}) : QQ^t = Q^tQ = I \right\}
+      \]
+    \end{column}
+    \begin{column}{.5\textwidth}
+      \begin{align*}
+        \Phi_\mathbb{1} &= \begin{pmatrix}
+          1 & 0 & 0 \\
+          0 & 1 & 0 \\
+          0 & 0 & 1
+        \end{pmatrix} = I \\[1em]
+        \Phi_\sigma &= \begin{pmatrix}
+          1 & 0 & 0 \\
+          0 & -1 & 0 \\
+          0 & 0 & 1
+        \end{pmatrix} \\[1em]
+        \Phi_r &= \begin{pmatrix}
+          \cos \alpha & -\sin \alpha & 0 \\
+          \sin \alpha & \cos \alpha & 0 \\
+          0 & 0 & 1 \\[1em]
+        \end{pmatrix}
+      \end{align*}
+    \end{column}
+  \end{columns}
+}
 
 \section{Kristalle}
 \begin{frame}[fragile]{}
@@ -178,11 +216,19 @@
 
           \end{tikzpicture}
       \end{center}
+    \end{column}
+    \begin{column}{.5\textwidth}
       Invariant (symmetrisch) unten Translation
       \[
         Q_i(\vec{r}) = \vec{r} + \vec{a}_i
       \]
+	    M\"ogliche Kristallstrukturen
     \end{column}
+  \end{columns}
+\end{frame}
+
+\begin{frame}[fragile]{}
+  \begin{columns}[T]
     \begin{column}{.5\textwidth}
       Wie kombiniert sich \(Q_i\) mit der anderen Symmetrien?
       \begin{center}
@@ -233,11 +279,6 @@
         n &= 1 - 2\cos\alpha
       \end{align*}
     \end{column}
-  \end{columns}
-\end{frame}
-
-\frame{
-  \begin{columns}[T]
     \begin{column}{.5\textwidth}
       Somit muss
       \[
@@ -247,10 +288,8 @@
         \alpha \in \left\{ 0, 60^\circ, 90^\circ, 120^\circ, 180^\circ \right\}
       \end{gather*}
     \end{column}
-    \begin{column}{.5\textwidth}
-    \end{column}
   \end{columns}
-}
+\end{frame}
 
 \section{Anwendungen}
 \begin{frame}[fragile]{}
-- 
cgit v1.2.1


From 262989abd634eddac1dae3974964c382c0301a94 Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Wed, 5 May 2021 16:17:06 +0200
Subject: Add venn diagram and fix typos

---
 vorlesungen/punktgruppen/slides.tex | 59 +++++++++++++++++++++++++------------
 1 file changed, 40 insertions(+), 19 deletions(-)

(limited to 'vorlesungen/punktgruppen/slides.tex')

diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
index 54798f1..d38065d 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -155,7 +155,7 @@
       \end{align*}
       Orthogonale Gruppe
       \[
-        O(n) = \left\{ Q \in \mathrm{GL}_n(\mathbb{R}) : QQ^t = Q^tQ = I \right\}
+        O(n) = \left\{ Q : QQ^t = Q^tQ = I \right\}
       \]
     \end{column}
     \begin{column}{.5\textwidth}
@@ -173,7 +173,7 @@
         \Phi_r &= \begin{pmatrix}
           \cos \alpha & -\sin \alpha & 0 \\
           \sin \alpha & \cos \alpha & 0 \\
-          0 & 0 & 1 \\[1em]
+          0 & 0 & 1
         \end{pmatrix}
       \end{align*}
     \end{column}
@@ -208,21 +208,40 @@
                 }
               }
             \end{scope}
-
             \draw[white, thick] (-1, -1) rectangle (4,3);
 
-            \draw[red!80!background, thick, ->] (N00) to node[midway, below] {\(\vec{a}_1\)} (N10);
-            \draw[cyan!80!background, thick, ->] (N00) to node[midway, left] {\(\vec{a}_2\)} (N01);
-
+            \draw[red!80!background, thick, ->] 
+              (N00) to node[midway, below] {\(\vec{a}_1\)} (N10);
+            \draw[cyan!80!background, thick, ->]
+              (N00) to node[midway, left] {\(\vec{a}_2\)} (N01);
           \end{tikzpicture}
       \end{center}
     \end{column}
     \begin{column}{.5\textwidth}
-      Invariant (symmetrisch) unten Translation
+      Invariant (symmetrisch) unter Translation
       \[
         Q_i(\vec{r}) = \vec{r} + \vec{a}_i
       \]
 	    M\"ogliche Kristallstrukturen
+      \begin{center}
+        \begin{tikzpicture}[]
+          \node[circle, dashed, draw = gray, 
+            thick, fill = background,
+            minimum size = 4cm] {};
+          \node[gray] at (.9,-1.2) {674};
+
+          \node[circle, draw = white, thick,
+            fill = orange!40!background,
+            xshift = -3mm, yshift = 2mm,
+            minimum size = 2.75cm] (A) {};
+          \node[white, yshift = 2mm] at (A) {230};
+
+          \node[circle, draw = white, thick, 
+            fill = red!20!background,
+            xshift = -5mm, yshift = -5mm,
+            minimum size = 1cm] {32};
+        \end{tikzpicture}
+      \end{center}
     \end{column}
   \end{columns}
 \end{frame}
@@ -272,21 +291,19 @@
           \node[above left, xshift=-2mm] at (X) {\(x\)};
         \end{tikzpicture}
       \end{center}
+    \end{column}
+    \begin{column}{.5\textwidth}
       Sei \(q = |\vec{Q}|\), \(\alpha = 2\pi/n\) und \(n \in \mathbb{N}\)
       \begin{align*}
         q' = n q &= q + 2x \\
         nq &= q + 2q\sin(\alpha - \pi/2) \\
         n &= 1 - 2\cos\alpha
       \end{align*}
-    \end{column}
-    \begin{column}{.5\textwidth}
       Somit muss
-      \[
-        \alpha = \cos^{-1}\left(\frac{m-1}{2}\right)
-      \]
-      \begin{gather*}
-        \alpha \in \left\{ 0, 60^\circ, 90^\circ, 120^\circ, 180^\circ \right\}
-      \end{gather*}
+      \begin{align*}
+        \alpha &= \cos^{-1}\left(\frac{n-1}{2}\right) \\[1em]
+        \alpha &\in \left\{ 0, 60^\circ, 90^\circ, 120^\circ, 180^\circ \right\}
+      \end{align*}
     \end{column}
   \end{columns}
 \end{frame}
@@ -386,9 +403,11 @@
 
       \node[white] (E) {\(\vec{E}_p\)};
       \begin{scope}[node distance = .5mm]
-        \node[blue!50, right = of E] {\(-\)};
-        \node[red!50, left = of E] {\(+\)};
+        \node[red!50, right = of E] {\(+\)};
+        \node[blue!50, left = of E] {\(-\)};
       \end{scope}
+      \draw[gray, thick, dotted] (E) to ++(0,2);
+      \draw[gray, thick, dotted] (E) to ++(0,-2);
     \end{scope}
 
     \begin{scope}[xshift=11cm, yshift=-4.5cm]
@@ -407,9 +426,11 @@
 
       \node[white] (E) {\(\vec{E}_p\)};
       \begin{scope}[node distance = .5mm]
-        \node[blue!50, right = of E] {\(-\)};
-        \node[red!50, left = of E] {\(+\)};
+        \node[red!50, right = of E] {\(+\)};
+        \node[blue!50, left = of E] {\(-\)};
       \end{scope}
+      \draw[gray, thick, dotted] (E) to ++(0,2);
+      \draw[gray, thick, dotted] (E) to ++(0,-2);
     \end{scope}
   \end{tikzpicture}
 \end{frame}
-- 
cgit v1.2.1


From c9e25f8c35027bde9af6f2ab72071dbdd21fa444 Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Wed, 5 May 2021 21:23:44 +0200
Subject: Add pauses and minor fixes

---
 vorlesungen/punktgruppen/slides.tex | 233 ++++++++++++++++++++----------------
 1 file changed, 132 insertions(+), 101 deletions(-)

(limited to 'vorlesungen/punktgruppen/slides.tex')

diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
index d38065d..cc62969 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -64,12 +64,11 @@
 \frame{\titlepage}
 \frame{\tableofcontents}
 
-\section{Einleitung}
 \frame{
   \begin{itemize}
-    \item Was heisst \emph{Symmetrie} in der Mathematik?
-    \item Wie kann ein Kristall modelliert werden?
-    \item Aus der Physik: Piezoelektrizit\"at
+    \item Was heisst \emph{Symmetrie} in der Mathematik? \pause
+    \item Wie kann ein Kristall modelliert werden? \pause
+    \item Aus der Physik: Piezoelektrizit\"at \pause
   \end{itemize}
   \begin{center}
     \begin{tikzpicture}
@@ -125,7 +124,7 @@
         \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 = -70, in = 70] node[midway, right] {\(U \neq 0\)} (n);
+        \draw[white, thick, ->] (p) to[out = -70, in = 70] node[midway, right] {\(U > 0\)} (n);
       \end{scope}
     \end{tikzpicture}
   \end{center}
@@ -148,16 +147,19 @@
       \[
         G = \left\{\mathbb{1}, r, \sigma, \dots \right\}
       \]
+      \pause
       Matrixdarstellung
       \begin{align*}
         \Phi : G &\to O(3) \\
         g &\mapsto \Phi_g
       \end{align*}
+      \pause
       Orthogonale Gruppe
       \[
         O(n) = \left\{ Q : QQ^t = Q^tQ = I \right\}
       \]
     \end{column}
+    \pause
     \begin{column}{.5\textwidth}
       \begin{align*}
         \Phi_\mathbb{1} &= \begin{pmatrix}
@@ -181,15 +183,31 @@
 }
 
 \section{Kristalle}
+\begin{frame}[fragile]{M\"ogliche Kristallstrukturen}
+  \begin{center}
+    \begin{tikzpicture}[]
+      \node[circle, dashed, draw = gray, 
+        thick, fill = background,
+        minimum size = 4cm] {};
+      \node[gray] at (.9,-1.2) {674};
+
+      \node[circle, draw = white, thick,
+        fill = orange!40!background,
+        xshift = -3mm, yshift = 2mm,
+        minimum size = 2.75cm] (A) {};
+      \node[white, yshift = 2mm] at (A) {230};
+
+      \node[circle, draw = white, thick, 
+        fill = red!20!background,
+        xshift = -5mm, yshift = -5mm,
+        minimum size = 1cm] {32};
+    \end{tikzpicture}
+  \end{center}
+\end{frame}
+
 \begin{frame}[fragile]{}
-  \begin{columns}[T]
+  \begin{columns}
     \begin{column}{.5\textwidth}
-      Kristallgitter:
-      \(n_i \in \mathbb{Z}\),
-      \(\vec{a}_i \in \mathbb{R}^3\)
-      \[
-        \vec{r} = n_1 \vec{a}_1 + n_2 \vec{a}_2 + n_3 \vec{a}_3
-      \]
       \begin{center}
           \begin{tikzpicture}[
               dot/.style = {
@@ -201,14 +219,14 @@
             ]
 
             \begin{scope}
-              \clip (-1,-1) rectangle (4,3);
-              \foreach \y in {-5,-4,...,5} {
-                \foreach \x in {-5,-4,...,5} {
+              \clip (-2,-2) rectangle (3,4);
+              \foreach \y in {-7,-6,...,7} {
+                \foreach \x in {-7,-6,...,7} {
                   \node[dot, xshift=3mm*\y] (N\x\y) at (\x, \y) {};
                 }
               }
             \end{scope}
-            \draw[white, thick] (-1, -1) rectangle (4,3);
+            \draw[white, thick] (-2, -2) rectangle (3,4);
 
             \draw[red!80!background, thick, ->] 
               (N00) to node[midway, below] {\(\vec{a}_1\)} (N10);
@@ -217,31 +235,21 @@
           \end{tikzpicture}
       \end{center}
     \end{column}
+    \pause
     \begin{column}{.5\textwidth}
-      Invariant (symmetrisch) unter Translation
+      Kristallgitter:
+      \(n_i \in \mathbb{Z}\),
+      \(\vec{a}_i \in \mathbb{R}^3\)
+      \[
+        \vec{r} = n_1 \vec{a}_1 + n_2 \vec{a}_2 + n_3 \vec{a}_3
+      \]
+      \vspace{1cm}
+      \pause
+      
+      Invariant unter Translation
       \[
         Q_i(\vec{r}) = \vec{r} + \vec{a}_i
       \]
-	    M\"ogliche Kristallstrukturen
-      \begin{center}
-        \begin{tikzpicture}[]
-          \node[circle, dashed, draw = gray, 
-            thick, fill = background,
-            minimum size = 4cm] {};
-          \node[gray] at (.9,-1.2) {674};
-
-          \node[circle, draw = white, thick,
-            fill = orange!40!background,
-            xshift = -3mm, yshift = 2mm,
-            minimum size = 2.75cm] (A) {};
-          \node[white, yshift = 2mm] at (A) {230};
-
-          \node[circle, draw = white, thick, 
-            fill = red!20!background,
-            xshift = -5mm, yshift = -5mm,
-            minimum size = 1cm] {32};
-        \end{tikzpicture}
-      \end{center}
     \end{column}
   \end{columns}
 \end{frame}
@@ -249,7 +257,9 @@
 \begin{frame}[fragile]{}
   \begin{columns}[T]
     \begin{column}{.5\textwidth}
-      Wie kombiniert sich \(Q_i\) mit der anderen Symmetrien?
+      \onslide<1->{
+        Wie kombiniert sich \(Q_i\) mit der anderen Symmetrien?
+      }
       \begin{center}
         \begin{tikzpicture}[
             dot/.style = {
@@ -260,50 +270,70 @@
             },
           ]
 
-          \node[dot] (A1) at (0,0) {};
-          \node[below left] at (A1) {\(A\)};
-
-          \node[dot] (A2) at (2.5,0) {};
-          \node[below right] at (A2) {\(A'\)};
-
-          \draw[red!80!background, thick, ->] 
-            (A1) to node[midway, below] {\(\vec{Q}\)} (A2);
-
-          \node[dot] (B1) at (120:2.5) {};
-          \node[above left] at (B1) {\(B\)};
-
-          \draw[green!70!background, thick, ->]
-            (A1) ++(.5,0) arc (0:120:.5) node[midway, above, xshift=1mm] {\(C_n\)};
-          \draw[red!80!background, dashed, thick, ->] (A1) to (B1);
+          \onslide<2->{
+            \node[dot] (A1) at (0,0) {};
+            \node[below left] at (A1) {\(A\)};
+          }
 
+          \onslide<3->{
+            \node[dot] (A2) at (2.5,0) {};
+            \node[below right] at (A2) {\(A'\)};
 
-          \node[dot] (B2) at ($(A2)+(60:2.5)$) {};
-          \node[above right] at (B2) {\(B'\)};
-
-          \draw[green!70!background, thick, dashed, ->] (A2) ++(-.5,0) arc (180:60:.5);
-          \draw[red!80!background, dashed, thick, ->] (A2) to (B2);
-
-          \draw[yellow!80!background, thick, ->] (B1) to node[above, midway] {\(\vec{Q}'\)} (B2);
-
+            \draw[red!80!background, thick, ->] 
+              (A1) to node[midway, below] {\(\vec{Q}\)} (A2);
+          }
+
+          \onslide<4->{
+            \node[dot] (B1) at (120:2.5) {};
+            \node[above left] at (B1) {\(B\)};
+
+            \draw[green!70!background, thick, ->]
+              (A1) ++(.5,0) arc (0:120:.5)
+              node[midway, above, xshift=1mm] {\(C_n\)};
+            \draw[red!80!background, dashed, thick, ->] (A1) to (B1);
+          }
+
+          \onslide<5->{
+            \node[dot] (B2) at ($(A2)+(60:2.5)$) {};
+            \node[above right] at (B2) {\(B'\)};
+
+            \draw[green!70!background, thick, dashed, ->]
+              (A2) ++(-.5,0) arc (180:60:.5);
+            \draw[red!80!background, dashed, thick, ->] (A2) to (B2);
+          }
+
+          \onslide<6->{
+            \draw[yellow!80!background, thick, ->]
+              (B1) to node[above, midway] {\(\vec{Q}'\)} (B2);
+          }
+
+          \onslide<7->{
           \draw[gray, dashed, thick] (A1) to (A1 |- B1) node (X) {};
           \draw[gray, dashed, thick] (A2) to (A2 |- B2);
+          }
 
-          \node[above left, xshift=-2mm] at (X) {\(x\)};
+          \onslide<8->{
+            \node[above left, xshift=-2mm] at (X) {\(x\)};
+          }
         \end{tikzpicture}
       \end{center}
     \end{column}
     \begin{column}{.5\textwidth}
-      Sei \(q = |\vec{Q}|\), \(\alpha = 2\pi/n\) und \(n \in \mathbb{N}\)
-      \begin{align*}
-        q' = n q &= q + 2x \\
-        nq &= q + 2q\sin(\alpha - \pi/2) \\
-        n &= 1 - 2\cos\alpha
-      \end{align*}
-      Somit muss
+      \onslide<9->{
+        Sei \(q = |\vec{Q}|\), \(\alpha = 2\pi/n\) und \(n \in \mathbb{N}\)
+      }
       \begin{align*}
-        \alpha &= \cos^{-1}\left(\frac{n-1}{2}\right) \\[1em]
-        \alpha &\in \left\{ 0, 60^\circ, 90^\circ, 120^\circ, 180^\circ \right\}
+        \onslide<10->{q' = n q &= q + 2x \\}
+        \onslide<11->{nq &= q + 2q\sin(\alpha - \pi/2) \\}
+        \onslide<12->{n &= 1 - 2\cos\alpha}
       \end{align*}
+      \onslide<13->{
+        Somit muss
+        \begin{align*}
+          \alpha &= \cos^{-1}\left(\frac{1-n}{2}\right) \\[1em]
+          \alpha &\in \left\{ 0, 60^\circ, 90^\circ, 120^\circ, 180^\circ \right\}
+        \end{align*}
+      }
     \end{column}
   \end{columns}
 \end{frame}
@@ -343,8 +373,9 @@
       negative/.style = { fill = blue!50 },
     ]
 
-    \node[font = {\large\bfseries}, align = center] (title) at (6,0) {Mit und Ohne\\ Symmetriezentrum};
+    \node[font = {\large\bfseries}, align = center] (title) at (5.5,0) {Mit und Ohne\\ Symmetriezentrum};
     \node[below = of title] {Polarisation Feld \(\vec{E}_p\)};
+    \pause
 
     \begin{scope}
       \matrix[nodes = { charge }, row sep = 8mm, column sep = 8mm] {
@@ -354,6 +385,7 @@
       };
       \draw[gray, dashed] (W) to (N) to (E) to (S) to (W);
     \end{scope}
+    \pause
 
     \begin{scope}[yshift=-4.5cm]
       \matrix[nodes = { charge }, row sep = 5mm, column sep = 1cm] {
@@ -372,6 +404,7 @@
 
       \draw[gray, dashed] (W) to (N) to (E) to (S) to (W);
     \end{scope}
+    \pause
 
     \begin{scope}[xshift=11cm]
       \foreach \x/\t [count=\i] in {60/positive, 120/negative, 180/positive, 240/negative, 300/positive, 360/negative} {
@@ -379,27 +412,23 @@
       }
 
       \draw[white] (C1) to (C2) to (C3) to (C4) to (C5) to (C6) to (C1);
-      \draw[gray, dashed] (C2) to (C4) to (C6) to (C2);
+      % \draw[gray, dashed] (C2) to (C4) to (C6) to (C2);
     \end{scope}
+    \pause
 
-    \begin{scope}[xshift=6cm, yshift=-4.5cm]
-      \node[charge, positive, yshift=-2.5mm] (C1) at ( 60:1.5cm) {};
-      \node[charge, negative, yshift=-2.5mm] (C2) at (120:1.5cm) {};
-      \node[charge, positive, xshift=-2.5mm] (C3) at (180:1.5cm) {};
-      \node[charge, negative, yshift= 2.5mm] (C4) at (240:1.5cm) {};
-      \node[charge, positive, yshift= 2.5mm] (C5) at (300:1.5cm) {};
-      \node[charge, negative, xshift= 2.5mm] (C6) at (360:1.5cm) {};
+    \begin{scope}[xshift=11cm, yshift=-4.5cm]
+      \node[charge, positive, yshift= 2.5mm] (C1) at ( 60:1.5cm) {};
+      \node[charge, negative, yshift= 2.5mm] (C2) at (120:1.5cm) {};
+      \node[charge, positive, xshift= 2.5mm] (C3) at (180:1.5cm) {};
+      \node[charge, negative, yshift=-2.5mm] (C4) at (240:1.5cm) {};
+      \node[charge, positive, yshift=-2.5mm] (C5) at (300:1.5cm) {};
+      \node[charge, negative, xshift=-2.5mm] (C6) at (360:1.5cm) {};
 
       \draw[white] (C1) to (C2) to (C3) to (C4) to (C5) to (C6) to (C1);
       % \draw[gray, dashed] (C2) to (C4) to (C6) to (C2);
 
-      \foreach \d in {C1, C2} {
-        \draw[orange, very thick, <-] (\d) to ++(0,.7);
-      }
-
-      \foreach \d in {C4, C5} {
-        \draw[orange, very thick, <-] (\d) to ++(0,-.7);
-      }
+      \draw[orange, very thick, <-] (C6) to ++(.7,0);
+      \draw[orange, very thick, <-] (C3) to ++(-.7,0);
 
       \node[white] (E) {\(\vec{E}_p\)};
       \begin{scope}[node distance = .5mm]
@@ -409,20 +438,26 @@
       \draw[gray, thick, dotted] (E) to ++(0,2);
       \draw[gray, thick, dotted] (E) to ++(0,-2);
     \end{scope}
+    \pause
 
-    \begin{scope}[xshift=11cm, yshift=-4.5cm]
-      \node[charge, positive, yshift= 2.5mm] (C1) at ( 60:1.5cm) {};
-      \node[charge, negative, yshift= 2.5mm] (C2) at (120:1.5cm) {};
-      \node[charge, positive, xshift= 2.5mm] (C3) at (180:1.5cm) {};
-      \node[charge, negative, yshift=-2.5mm] (C4) at (240:1.5cm) {};
-      \node[charge, positive, yshift=-2.5mm] (C5) at (300:1.5cm) {};
-      \node[charge, negative, xshift=-2.5mm] (C6) at (360:1.5cm) {};
+    \begin{scope}[xshift=5.5cm, yshift=-4.5cm]
+      \node[charge, positive, yshift=-2.5mm] (C1) at ( 60:1.5cm) {};
+      \node[charge, negative, yshift=-2.5mm] (C2) at (120:1.5cm) {};
+      \node[charge, positive, xshift=-2.5mm] (C3) at (180:1.5cm) {};
+      \node[charge, negative, yshift= 2.5mm] (C4) at (240:1.5cm) {};
+      \node[charge, positive, yshift= 2.5mm] (C5) at (300:1.5cm) {};
+      \node[charge, negative, xshift= 2.5mm] (C6) at (360:1.5cm) {};
 
       \draw[white] (C1) to (C2) to (C3) to (C4) to (C5) to (C6) to (C1);
       % \draw[gray, dashed] (C2) to (C4) to (C6) to (C2);
 
-      \draw[orange, very thick, <-] (C6) to ++(.7,0);
-      \draw[orange, very thick, <-] (C3) to ++(-.7,0);
+      \foreach \d in {C1, C2} {
+        \draw[orange, very thick, <-] (\d) to ++(0,.7);
+      }
+
+      \foreach \d in {C4, C5} {
+        \draw[orange, very thick, <-] (\d) to ++(0,-.7);
+      }
 
       \node[white] (E) {\(\vec{E}_p\)};
       \begin{scope}[node distance = .5mm]
@@ -462,15 +497,11 @@
       \]
       Anisotropisch Dielektrikum
       \[
-        (\ten{K}\ten{\varepsilon})\vec{E} = \frac{\omega^2}{\mu k^2} \vec{E}
+        (\ten{K}\ten{\varepsilon})\vec{E} = \frac{k^2}{\mu \omega^2} \vec{E}
       \]
       \[
         \vec{E} \in U_\lambda \implies (\ten{K}\ten{\varepsilon}) \vec{E} = \lambda \vec{E}
       \]
-      \"Ahenlich auch in der Mechanik
-      \[
-        \vec{F} = \kappa \vec{x} \quad \text{(Hooke)}
-      \]
     \end{column}
   \end{columns}
 }
-- 
cgit v1.2.1


From 8f862d9be3117979c9694544cca0afa8d2e53cb3 Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Wed, 5 May 2021 23:07:28 +0200
Subject: Add (back) slide for algebraic symmetries

Probably won't be used but still.
---
 vorlesungen/punktgruppen/slides.tex | 51 +++++++++++++++++++++++++++++++++++++
 1 file changed, 51 insertions(+)

(limited to 'vorlesungen/punktgruppen/slides.tex')

diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
index cc62969..8edaff6 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -135,6 +135,57 @@
 
 \section{Algebraische Symmetrien}
 %% Made in video
+\frame{
+  \begin{columns}[T]
+    \begin{column}{.5\textwidth}
+      Produkt mit \(i\)
+      \begin{align*}
+        1 \cdot i &= i \\
+        i \cdot i &= -1 \\
+        -1 \cdot i &= -i \\
+        -i \cdot i &= 1
+      \end{align*}
+      \pause
+      %
+      Gruppe
+      \begin{align*}
+        G &= \left\{
+          1, i, -1, -i
+        \right\} \\
+        &= \left\{
+          1, i, i^2, i^3
+        \right\} \\
+        C_4 &= \left\{
+          \mathbb{1}, r, r^2, r^3
+        \right\}
+      \end{align*}
+      \pause
+    \end{column}
+    \begin{column}{.5\textwidth}
+      Darstellung \(\phi : C_4 \to G\)
+      \begin{align*}
+        \phi(\mathbb{1}) &= 1 & \phi(r^2) &= i^2 \\
+        \phi(r) &= i & \phi(r^3) &= i^3
+      \end{align*}
+      \pause
+      %
+      Homomorphismus
+      \begin{align*}
+        \phi(r \circ \mathbb{1}) &= \phi(r) \cdot \phi(\mathbb{1}) \\
+        &= i \cdot 1
+      \end{align*}
+      \pause
+      %
+      \(\phi\) ist bijektiv \(\implies C_4 \cong G\)
+			\pause
+			%
+			\begin{align*}
+				\psi : C_4 &\to (\mathbb{Z}/4\mathbb{Z}, +) \\
+				\psi(\mathbb{1}\circ r^2) &= 0 + 2 \pmod{4}
+			\end{align*}
+    \end{column}
+  \end{columns}
+}
 
 \section{3D Symmetrien}
 %% Made in video
-- 
cgit v1.2.1


From 1d952ad204000bd84383564cbd4240dcb6982738 Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Wed, 5 May 2021 23:51:37 +0200
Subject: Add placeholder slides for video parts and update gitignore

---
 vorlesungen/punktgruppen/slides.tex | 10 ++++++++++
 1 file changed, 10 insertions(+)

(limited to 'vorlesungen/punktgruppen/slides.tex')

diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
index 8edaff6..3aa6d83 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -132,6 +132,11 @@
 
 \section{2D Symmetrien}
 %% Made in video
+{
+  \usebackgroundtemplate{
+    \includegraphics[height=\paperheight]{media/images/nosignal}}
+  \frame{}
+}
 
 \section{Algebraische Symmetrien}
 %% Made in video
@@ -189,6 +194,11 @@
 
 \section{3D Symmetrien}
 %% Made in video
+{
+  \usebackgroundtemplate{
+    \includegraphics[height=\paperheight]{media/images/nosignal}}
+  \frame{}
+}
 
 \section{Matrizen}
 \frame{
-- 
cgit v1.2.1


From 965fe8cb04683c1efea1b955af93485e7860d235 Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Thu, 6 May 2021 00:04:07 +0200
Subject: Add link to slides

---
 vorlesungen/punktgruppen/slides.tex | 9 ++++++++-
 1 file changed, 8 insertions(+), 1 deletion(-)

(limited to 'vorlesungen/punktgruppen/slides.tex')

diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
index 3aa6d83..da13003 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -61,7 +61,14 @@
 
 % Slides
 \begin{document}
-\frame{\titlepage}
+\frame{
+  \titlepage
+  \vfill
+  \begin{center}
+    \small \color{gray}
+    Slides: \texttt{s.0hm.ch/ctBsD}
+  \end{center}
+}
 \frame{\tableofcontents}
 
 \frame{
-- 
cgit v1.2.1


From b879ffd58aa2c74b8f7b199edfa4b108b88c6e0b Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Fri, 7 May 2021 00:12:11 +0200
Subject: Create slide to show all point groups

---
 vorlesungen/punktgruppen/slides.tex | 265 +++++++++++++++++++++++++++++++++++-
 1 file changed, 263 insertions(+), 2 deletions(-)

(limited to 'vorlesungen/punktgruppen/slides.tex')

diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
index da13003..08b6ecb 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -1,4 +1,4 @@
-\documentclass[12pt, xcolor, aspectratio=169]{beamer}
+\documentclass[12pt, xcolor, aspectratio=169, handout]{beamer}
 
 % language
 \usepackage{polyglossia}
@@ -8,8 +8,16 @@
 \usepackage{tikz}
 \usetikzlibrary{positioning}
 \usetikzlibrary{arrows.meta}
+\usetikzlibrary{shapes.misc}
 \usetikzlibrary{calc}
 
+\usetikzlibrary{external}
+\tikzexternalize[
+  mode = graphics if exists,
+  figure list = true,
+  prefix=build/
+]
+
 % Theme
 \beamertemplatenavigationsymbolsempty
 
@@ -399,13 +407,266 @@
         Somit muss
         \begin{align*}
           \alpha &= \cos^{-1}\left(\frac{1-n}{2}\right) \\[1em]
-          \alpha &\in \left\{ 0, 60^\circ, 90^\circ, 120^\circ, 180^\circ \right\}
+          \alpha &\in \left\{ 0, 60^\circ, 90^\circ, 120^\circ, 180^\circ \right\} \\
+          n &\in \left\{ 1, 2, 3, 4, 6 \right\}
         \end{align*}
       }
     \end{column}
   \end{columns}
 \end{frame}
 
+{
+  \usebackgroundtemplate[fragile]{
+    \begin{tikzpicture}[
+        overlay,
+        xshift = .45\paperwidth,
+        yshift = .47\paperheight,
+        classcirc/.style = {
+          draw = gray, thick, circle,
+          minimum size = 12mm,
+          inner sep = 0pt, outer sep = 0pt,
+        },
+        classlabel/.style = {
+          below right = 5mm
+        },
+        round/.style = {
+          draw = yellow, thick, circle,
+          minimum size = 1mm,
+          inner sep = 0pt, outer sep = 0pt,
+        },
+        cross/.style = {
+          cross out, draw = magenta, thick,
+          minimum size = 1mm, 
+          inner sep = 0pt, outer sep = 0pt
+        },
+      ]
+      \matrix [row sep = 3mm, column sep = 0mm] {
+        \node[classcirc] (C1)  {} node[classlabel] {\(C_{1}\)};  & 
+        \node[classcirc] (C2)  {} node[classlabel] {\(C_{2}\)};  &
+        \node[classcirc] (C3)  {} node[classlabel] {\(C_{3}\)};  &
+        \node[classcirc] (Ci)  {} node[classlabel] {\(C_{i}\)};  &
+
+        \node[classcirc] (Cs)  {} node[classlabel] {\(C_{s}\)};  &
+        \node[classcirc] (C3i) {} node[classlabel] {\(C_{3i}\)}; &
+        \node[classcirc] (C2h) {} node[classlabel] {\(C_{2h}\)}; &
+        \node[classcirc] (D2)  {} node[classlabel] {\(D_{2}\)};  \\
+
+        \node[classcirc] (D3d) {} node[classlabel] {\(D_{3d}\)}; &
+        \node[classcirc] (C2v) {} node[classlabel] {\(C_{2v}\)}; & 
+        \node[classcirc] (D2h) {} node[classlabel] {\(D_{2h}\)}; & 
+        \node[classcirc] (D3)  {} node[classlabel] {\(D_{3}\)};  &
+
+        \node[classcirc] (C4)  {} node[classlabel] {\(C_{4}\)};  &
+        \node[classcirc] (C6)  {} node[classlabel] {\(C_{6}\)};  &
+        \node[classcirc] (D3dP) {} node[classlabel] {\(D_{3d}\)}; &
+        \node[classcirc] (S4)  {} node[classlabel] {\(S_{4}\)};  \\
+
+        \node[classcirc] (S3)  {} node[classlabel] {\(S_{3}\)};  &
+        \node[classcirc, dashed] (T)   {} node[classlabel] {\(T_{}\)};   &
+        \node[classcirc] (C4h) {} node[classlabel] {\(C_{4h}\)}; &
+        \node[classcirc] (C6h) {} node[classlabel] {\(C_{6h}\)}; &
+
+        \node[classcirc, dashed] (Th)  {} node[classlabel] {\(T_{h}\)};  &
+        \node[classcirc] (C4v) {} node[classlabel] {\(C_{4v}\)}; &
+        \node[classcirc] (C6v) {} node[classlabel] {\(C_{6v}\)}; &
+        \node[classcirc, dashed] (Td)  {} node[classlabel] {\(T_{d}\)};  \\
+        
+        \node[classcirc] (D2d) {} node[classlabel] {\(D_{2d}\)}; &
+        \node[classcirc] (D3h) {} node[classlabel] {\(D_{3h}\)}; &
+        \node[classcirc, dashed] (O)   {} node[classlabel] {\(O_{}\)};   &
+        \node[classcirc] (D4)  {} node[classlabel] {\(D_{4}\)};  &
+
+        \node[classcirc] (D6)  {} node[classlabel] {\(D_{6}\)};  &
+        \node[classcirc, dashed] (Oh)  {} node[classlabel] {\(O_{h}\)};  &
+        \node[classcirc] (D4h) {} node[classlabel] {\(D_{4h}\)}; &
+        \node[classcirc] (D6h) {} node[classlabel] {\(D_{6h}\)}; \\
+      };
+
+
+      \node[cross] at ($(C1)+(4mm,0)$) {};
+
+      
+      \node[cross] at ($(C2)+(4mm,0)$) {};
+      \node[cross] at ($(C2)-(4mm,0)$) {};
+
+
+      \node[cross] at ($(C3)+(  0:4mm)$) {};
+      \node[cross] at ($(C3)+(120:4mm)$) {};
+      \node[cross] at ($(C3)+(240:4mm)$) {};
+
+
+      \node[cross] at ($(Ci)+(4mm,0)$) {};
+      \node[round] at ($(Ci)-(4mm,0)$) {};
+
+
+      \node[cross] at ($(Cs)+(4mm,0)$) {};
+      \node[round] at ($(Cs)+(4mm,0)$) {};
+
+
+      \node[cross] at ($(C3i)+(  0:4mm)$) {};
+      \node[cross] at ($(C3i)+(120:4mm)$) {};
+      \node[cross] at ($(C3i)+(240:4mm)$) {};
+      \node[round] at ($(C3i)+( 60:4mm)$) {};
+      \node[round] at ($(C3i)+(180:4mm)$) {};
+      \node[round] at ($(C3i)+(300:4mm)$) {};
+
+
+      \node[cross] at ($(C2h)+(4mm,0)$) {};
+      \node[cross] at ($(C2h)-(4mm,0)$) {};
+      \node[round] at ($(C2h)+(4mm,0)$) {};
+      \node[round] at ($(C2h)-(4mm,0)$) {};
+
+
+      \node[cross] at ($(D2)+( 20:4mm)$) {};
+      \node[cross] at ($(D2)+(200:4mm)$) {};
+      \node[round] at ($(D2)+(160:4mm)$) {};
+      \node[round] at ($(D2)+(340:4mm)$) {};
+
+
+      \foreach \x in {0, 120, 240} {
+        \node[cross] at ($(D3d)+({\x+15}:4mm)$) {};
+        \node[cross] at ($(D3d)+({\x-15}:4mm)$) {};
+      }
+
+
+      \foreach \x in {0, 180} {
+        \node[cross] at ($(C2v)+({\x+15}:4mm)$) {};
+        \node[cross] at ($(C2v)+({\x-15}:4mm)$) {};
+      }
+
+
+      \foreach \x in {0, 180} {
+        \node[cross] at ($(D2h)+({\x+15}:4mm)$) {};
+        \node[cross] at ($(D2h)+({\x-15}:4mm)$) {};
+        \node[round] at ($(D2h)+({\x+15}:4mm)$) {};
+        \node[round] at ($(D2h)+({\x-15}:4mm)$) {};
+      }
+
+
+      \foreach \x in {0, 120, 240} {
+        \node[cross] at ($(D3)+({\x+15}:4mm)$) {};
+        \node[round] at ($(D3)+({\x-15}:4mm)$) {};
+      }
+
+
+      \foreach \x in {0, 90, 180, 270} {
+        \node[cross] at ($(C4)+(\x:4mm)$) {};
+      }
+
+
+      \foreach \x in {0, 60, 120, 180, 240, 300} {
+        \node[cross] at ($(C6)+(\x:4mm)$) {};
+      }
+
+
+      \foreach \x in {0, 120, 240} {
+        \node[cross] at ($(D3dP)+({\x+15}:4mm)$) {};
+        \node[cross] at ($(D3dP)+({\x-15}:4mm)$) {};
+        \node[round] at ($(D3dP)+({\x+15+60}:4mm)$) {};
+        \node[round] at ($(D3dP)+({\x-15+60}:4mm)$) {};
+      }
+
+
+      \node[cross] at ($(S4)+(4mm,0)$) {};
+      \node[cross] at ($(S4)-(4mm,0)$) {};
+      \node[round] at ($(S4)+(0,4mm)$) {};
+      \node[round] at ($(S4)-(0,4mm)$) {};
+
+
+      \foreach \x in {0, 120, 240} {
+        \node[cross] at ($(S3)+(\x:4mm)$) {};
+        \node[round] at ($(S3)+(\x:4mm)$) {};
+      }
+
+
+      %% TODO: T
+
+
+      \foreach \x in {0, 90, 180, 270} {
+        \node[cross] at ($(C4h)+(\x:4mm)$) {};
+        \node[round] at ($(C4h)+(\x:4mm)$) {};
+      }
+
+
+      \foreach \x in {0, 60, 120, 180, 240, 300} {
+        \node[cross] at ($(C6h)+(\x:4mm)$) {};
+        \node[round] at ($(C6h)+(\x:4mm)$) {};
+      }
+
+
+      %% TODO: Th
+
+
+      \foreach \x in {0, 90, 180, 270} {
+        \node[cross] at ($(C4v)+(\x+15:4mm)$) {};
+        \node[cross] at ($(C4v)+(\x-15:4mm)$) {};
+      }
+
+
+
+      \foreach \x in {0, 60, 120, 180, 240, 300} {
+        \node[cross] at ($(C6v)+(\x+10:4mm)$) {};
+        \node[cross] at ($(C6v)+(\x-10:4mm)$) {};
+      }
+
+
+      %% TODO: Td
+
+
+      \foreach \x in {0, 180} {
+        \node[cross] at ($(D2d)+({\x+15}:4mm)$) {};
+        \node[round] at ($(D2d)+({\x-15}:4mm)$) {};
+
+        \node[round] at ($(D2d)+({\x+15+90}:4mm)$) {};
+        \node[cross] at ($(D2d)+({\x-15+90}:4mm)$) {};
+      }
+
+
+      \foreach \x in {0, 120, 240} {
+        \node[cross] at ($(D3h)+({\x+15}:4mm)$) {};
+        \node[cross] at ($(D3h)+({\x-15}:4mm)$) {};
+        \node[round] at ($(D3h)+({\x+15}:4mm)$) {};
+        \node[round] at ($(D3h)+({\x-15}:4mm)$) {};
+      }
+
+
+      %% TODO: O
+
+
+      \foreach \x in {0, 90, 180, 270} {
+        \node[cross] at ($(D4)+({\x+15}:4mm)$) {};
+        \node[round] at ($(D4)+({\x-15}:4mm)$) {};
+      }
+
+      \foreach \x in {0, 60, 120, 180, 240, 300} {
+        \node[cross] at ($(D6)+({\x+10}:4mm)$) {};
+        \node[round] at ($(D6)+({\x-10}:4mm)$) {};
+      }
+
+
+      % TODO Oh
+
+
+      \foreach \x in {0, 90, 180, 270} {
+        \node[cross] at ($(D4h)+(\x+15:4mm)$) {};
+        \node[cross] at ($(D4h)+(\x-15:4mm)$) {};
+        \node[round] at ($(D4h)+(\x+15:4mm)$) {};
+        \node[round] at ($(D4h)+(\x-15:4mm)$) {};
+      }
+
+
+      \foreach \x in {0, 60, 120, 180, 240, 300} {
+        \node[cross] at ($(D6h)+({\x+10}:4mm)$) {};
+        \node[cross] at ($(D6h)+({\x-10}:4mm)$) {};
+        \node[round] at ($(D6h)+({\x+10}:4mm)$) {};
+        \node[round] at ($(D6h)+({\x-10}:4mm)$) {};
+      }
+    \end{tikzpicture}
+  }
+  \begin{frame}[fragile]{}
+  \end{frame}
+}
+
 \section{Anwendungen}
 \begin{frame}[fragile]{}
   \centering
-- 
cgit v1.2.1


From 84f60f0f078481b05f1305ceff9565f2e7dd7471 Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Fri, 7 May 2021 17:54:43 +0200
Subject: Striptease

---
 vorlesungen/punktgruppen/slides.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

(limited to 'vorlesungen/punktgruppen/slides.tex')

diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
index 08b6ecb..dbcf40f 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -1,4 +1,4 @@
-\documentclass[12pt, xcolor, aspectratio=169, handout]{beamer}
+\documentclass[12pt, xcolor, aspectratio=169]{beamer}
 
 % language
 \usepackage{polyglossia}
-- 
cgit v1.2.1


From f751b6fa47c197216ef5d3faa617dbf9be4dd695 Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Sat, 8 May 2021 01:09:30 +0200
Subject: Minor changes to slides

---
 vorlesungen/punktgruppen/slides.tex | 156 +++++++++++++++++++-----------------
 1 file changed, 84 insertions(+), 72 deletions(-)

(limited to 'vorlesungen/punktgruppen/slides.tex')

diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
index dbcf40f..01d59f4 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -259,73 +259,59 @@
 }
 
 \section{Kristalle}
-\begin{frame}[fragile]{M\"ogliche Kristallstrukturen}
-  \begin{center}
-    \begin{tikzpicture}[]
-      \node[circle, dashed, draw = gray, 
-        thick, fill = background,
-        minimum size = 4cm] {};
-      \node[gray] at (.9,-1.2) {674};
-
-      \node[circle, draw = white, thick,
-        fill = orange!40!background,
-        xshift = -3mm, yshift = 2mm,
-        minimum size = 2.75cm] (A) {};
-      \node[white, yshift = 2mm] at (A) {230};
-
-      \node[circle, draw = white, thick, 
-        fill = red!20!background,
-        xshift = -5mm, yshift = -5mm,
-        minimum size = 1cm] {32};
-    \end{tikzpicture}
-  \end{center}
-\end{frame}
-
 \begin{frame}[fragile]{}
   \begin{columns}
-    \begin{column}{.5\textwidth}
-      \begin{center}
-          \begin{tikzpicture}[
-              dot/.style = {
-                draw, circle, thick, white, fill = gray!40!background,
-                minimum size = 2mm,
-                inner sep = 0pt,
-                outer sep = 1mm,
-              },
-            ]
-
-            \begin{scope}
-              \clip (-2,-2) rectangle (3,4);
-              \foreach \y in {-7,-6,...,7} {
-                \foreach \x in {-7,-6,...,7} {
-                  \node[dot, xshift=3mm*\y] (N\x\y) at (\x, \y) {};
+    \onslide<1->{
+      \begin{column}{.5\textwidth}
+        \begin{center}
+            \begin{tikzpicture}[
+                dot/.style = {
+                  draw, circle, thick, white, fill = gray!40!background,
+                  minimum size = 2mm,
+                  inner sep = 0pt,
+                  outer sep = 1mm,
+                },
+              ]
+
+              \begin{scope}
+                \clip (-2,-2) rectangle (3,4);
+                \foreach \y in {-7,-6,...,7} {
+                  \foreach \x in {-7,-6,...,7} {
+                    \node[dot, xshift=3mm*\y] (N\x\y) at (\x, \y) {};
+                  }
                 }
-              }
-            \end{scope}
-            \draw[white, thick] (-2, -2) rectangle (3,4);
-
-            \draw[red!80!background, thick, ->] 
-              (N00) to node[midway, below] {\(\vec{a}_1\)} (N10);
-            \draw[cyan!80!background, thick, ->]
-              (N00) to node[midway, left] {\(\vec{a}_2\)} (N01);
-          \end{tikzpicture}
-      \end{center}
-    \end{column}
-    \pause
+              \end{scope}
+              \draw[white, thick] (-2, -2) rectangle (3,4);
+
+              \draw[red!80!background, thick, ->] 
+                (N00) to node[midway, below] {\(\vec{a}_1\)} (N10);
+              \draw[cyan!80!background, thick, ->]
+                (N00) to node[midway, left] {\(\vec{a}_2\)} (N01);
+            \end{tikzpicture}
+        \end{center}
+      \end{column}
+    }
     \begin{column}{.5\textwidth}
-      Kristallgitter:
-      \(n_i \in \mathbb{Z}\),
-      \(\vec{a}_i \in \mathbb{R}^3\)
-      \[
-        \vec{r} = n_1 \vec{a}_1 + n_2 \vec{a}_2 + n_3 \vec{a}_3
-      \]
+      \onslide<2->{
+        Kristallgitter:
+        \(n_i \in \mathbb{Z}\),
+      }
+      \onslide<3->{
+        \(\vec{a}_i \in \mathbb{R}^3\)
+      }
+      \onslide<2->{
+        \[
+          \vec{r} = n_1 \vec{a}_1 + n_2 \vec{a}_2 \onslide<3->{+ n_3 \vec{a}_3}
+        \]
+      }
       \vspace{1cm}
-      \pause
-      
-      Invariant unter Translation
-      \[
-        Q_i(\vec{r}) = \vec{r} + \vec{a}_i
-      \]
+
+      \onslide<4->{
+        Invariant unter Translation
+        \[
+          Q_i(\vec{r}) = \vec{r} + \vec{a}_i
+        \]
+      }
     \end{column}
   \end{columns}
 \end{frame}
@@ -383,23 +369,21 @@
               (B1) to node[above, midway] {\(\vec{Q}'\)} (B2);
           }
 
-          \onslide<7->{
-          \draw[gray, dashed, thick] (A1) to (A1 |- B1) node (X) {};
-          \draw[gray, dashed, thick] (A2) to (A2 |- B2);
-          }
-
-          \onslide<8->{
-            \node[above left, xshift=-2mm] at (X) {\(x\)};
+          \onslide<10->{
+		    \draw[gray, dashed, thick] (A1) to (A1 |- B1) node (Xl) {};
+			\draw[gray, dashed, thick] (A2) to (A2 |- B2) node (Xr) {};
+            \node[above left, xshift=-2mm] at (Xl) {\(x\)};
+            \node[above right, xshift= 2mm] at (Xr) {\(x\)};
           }
         \end{tikzpicture}
       \end{center}
     \end{column}
     \begin{column}{.5\textwidth}
-      \onslide<9->{
+      \onslide<7->{
         Sei \(q = |\vec{Q}|\), \(\alpha = 2\pi/n\) und \(n \in \mathbb{N}\)
       }
       \begin{align*}
-        \onslide<10->{q' = n q &= q + 2x \\}
+        \onslide<9->{q' = n q \onslide<10->{&= q + 2x \\}}
         \onslide<11->{nq &= q + 2q\sin(\alpha - \pi/2) \\}
         \onslide<12->{n &= 1 - 2\cos\alpha}
       \end{align*}
@@ -415,6 +399,34 @@
   \end{columns}
 \end{frame}
 
+\begin{frame}[fragile]{M\"ogliche Kristallstrukturen}
+  \begin{center}
+    \begin{tikzpicture}[]
+      \node[circle, dashed, draw = gray, 
+        thick, fill = background,
+        minimum size = 4cm] {};
+      \node[gray] at (.9,-1.2) {674};
+
+      \node[circle, draw = white, thick,
+        fill = orange!40!background,
+        xshift = -3mm, yshift = 2mm,
+        minimum size = 2.75cm,
+        outer sep = 1mm] (A) {};
+      \node[white, yshift = 2mm] at (A) {230};
+      \node[white, font=\large, above right = of A] (Al) {Raumgruppe};
+      \draw[white, thick, ->] (Al.west) to[out=180, in=60] (A);
+
+      \node[circle, draw = white, thick, 
+        fill = red!20!background,
+        xshift = -5mm, yshift = -5mm,
+        minimum size = 1cm,
+        outer sep = 1mm] (B) {32};
+      \node[white, font=\large, below left = of B, xshift=-4mm] (Bl) {Kristallklassen};
+      \draw[white, thick, ->] (Bl.east) to[out = 0, in = 180] (B);
+    \end{tikzpicture}
+  \end{center}
+\end{frame}
+
 {
   \usebackgroundtemplate[fragile]{
     \begin{tikzpicture}[
@@ -678,7 +690,7 @@
     ]
 
     \matrix [nodes = {box, align = center}, column sep = 1cm, row sep = 1.5cm] {
-      & \node (A) {32 Punktgruppen}; \\
+      & \node (A) {32 Kristallklassen}; \\
       \node (B) {11 Mit\\ Inversionszentrum}; & \node (C) {21 Ohne\\ Inversionszentrum}; \\
       & \node[fill=red!20!background] (D) {20 Piezoelektrisch}; & \node (E) {1 Nicht\\ piezoelektrisch}; \\
     };
-- 
cgit v1.2.1


From f200f1bdb1b14bfcd9c3056d6d0a65f11a7a5ecc Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Sat, 8 May 2021 14:27:54 +0200
Subject: Little fix

---
 vorlesungen/punktgruppen/slides.tex | 49 +++++++++++++++++++------------------
 1 file changed, 25 insertions(+), 24 deletions(-)

(limited to 'vorlesungen/punktgruppen/slides.tex')

diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
index 01d59f4..ddc7ed1 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -715,7 +715,6 @@
     ]
 
     \node[font = {\large\bfseries}, align = center] (title) at (5.5,0) {Mit und Ohne\\ Symmetriezentrum};
-    \node[below = of title] {Polarisation Feld \(\vec{E}_p\)};
     \pause
 
     \begin{scope}
@@ -728,35 +727,18 @@
     \end{scope}
     \pause
 
-    \begin{scope}[yshift=-4.5cm]
-      \matrix[nodes = { charge }, row sep = 5mm, column sep = 1cm] {
-        \node[positive] (NW) {}; & \node[negative] (N) {}; & \node [positive] (NE) {}; \\
-        \node[negative] (W) {}; & \node[positive] {}; & \node [negative] (E) {}; \\
-        \node[positive] (SW) {}; & \node[negative] (S) {}; & \node [positive] (SE) {}; \\
-      };
-
-      \foreach \d in {NW, N, NE} {
-        \draw[orange, very thick, <-] (\d) to ++(0,.7);
-      }
-
-      \foreach \d in {SW, S, SE} {
-        \draw[orange, very thick, <-] (\d) to ++(0,-.7);
-      }
-
-      \draw[gray, dashed] (W) to (N) to (E) to (S) to (W);
-    \end{scope}
-    \pause
-
     \begin{scope}[xshift=11cm]
       \foreach \x/\t [count=\i] in {60/positive, 120/negative, 180/positive, 240/negative, 300/positive, 360/negative} {
         \node[charge, \t] (C\i) at (\x:1.5cm) {};
       }
 
       \draw[white] (C1) to (C2) to (C3) to (C4) to (C5) to (C6) to (C1);
+      \node[circle, draw=gray, fill=gray, outer sep = 0, inner sep = 0, minimum size = 3mm] {};
       % \draw[gray, dashed] (C2) to (C4) to (C6) to (C2);
     \end{scope}
     \pause
 
+    \node[below = of title] {Polarisation Feld \(\vec{E}_p\)};
     \begin{scope}[xshift=11cm, yshift=-4.5cm]
       \node[charge, positive, yshift= 2.5mm] (C1) at ( 60:1.5cm) {};
       \node[charge, negative, yshift= 2.5mm] (C2) at (120:1.5cm) {};
@@ -776,8 +758,27 @@
         \node[red!50, right = of E] {\(+\)};
         \node[blue!50, left = of E] {\(-\)};
       \end{scope}
-      \draw[gray, thick, dotted] (E) to ++(0,2);
-      \draw[gray, thick, dotted] (E) to ++(0,-2);
+      % \draw[gray, thick, dotted] (E) to ++(0,2);
+      % \draw[gray, thick, dotted] (E) to ++(0,-2);
+    \end{scope}
+    \pause
+
+    \begin{scope}[yshift=-4.5cm]
+      \matrix[nodes = { charge }, row sep = 5mm, column sep = 1cm] {
+        \node[positive] (NW) {}; & \node[negative] (N) {}; & \node [positive] (NE) {}; \\
+        \node[negative] (W) {}; & \node[positive] {}; & \node [negative] (E) {}; \\
+        \node[positive] (SW) {}; & \node[negative] (S) {}; & \node [positive] (SE) {}; \\
+      };
+
+      \foreach \d in {NW, N, NE} {
+        \draw[orange, very thick, <-] (\d) to ++(0,.7);
+      }
+
+      \foreach \d in {SW, S, SE} {
+        \draw[orange, very thick, <-] (\d) to ++(0,-.7);
+      }
+
+      \draw[gray, dashed] (W) to (N) to (E) to (S) to (W);
     \end{scope}
     \pause
 
@@ -805,8 +806,8 @@
         \node[red!50, right = of E] {\(+\)};
         \node[blue!50, left = of E] {\(-\)};
       \end{scope}
-      \draw[gray, thick, dotted] (E) to ++(0,2);
-      \draw[gray, thick, dotted] (E) to ++(0,-2);
+      % \draw[gray, thick, dotted] (E) to ++(0,2);
+      % \draw[gray, thick, dotted] (E) to ++(0,-2);
     \end{scope}
   \end{tikzpicture}
 \end{frame}
-- 
cgit v1.2.1


From 5ea80792f7fea3d05b62239cb5d6220fb43b3d41 Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Sat, 8 May 2021 14:58:28 +0200
Subject: Piezoelectricity is tricky

---
 vorlesungen/punktgruppen/slides.tex | 81 ++++++++++++++++++++-----------------
 1 file changed, 43 insertions(+), 38 deletions(-)

(limited to 'vorlesungen/punktgruppen/slides.tex')

diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
index ddc7ed1..e15dd9a 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -738,20 +738,28 @@
     \end{scope}
     \pause
 
+	%% 
     \node[below = of title] {Polarisation Feld \(\vec{E}_p\)};
+
+	%% hex with vertical pressure
     \begin{scope}[xshift=11cm, yshift=-4.5cm]
-      \node[charge, positive, yshift= 2.5mm] (C1) at ( 60:1.5cm) {};
-      \node[charge, negative, yshift= 2.5mm] (C2) at (120:1.5cm) {};
-      \node[charge, positive, xshift= 2.5mm] (C3) at (180:1.5cm) {};
-      \node[charge, negative, yshift=-2.5mm] (C4) at (240:1.5cm) {};
-      \node[charge, positive, yshift=-2.5mm] (C5) at (300:1.5cm) {};
-      \node[charge, negative, xshift=-2.5mm] (C6) at (360:1.5cm) {};
+      \node[charge, positive, yshift=-2.5mm] (C1) at ( 60:1.5cm) {};
+      \node[charge, negative, yshift=-2.5mm] (C2) at (120:1.5cm) {};
+      \node[charge, positive, xshift=-2.5mm] (C3) at (180:1.5cm) {};
+      \node[charge, negative, yshift= 2.5mm] (C4) at (240:1.5cm) {};
+      \node[charge, positive, yshift= 2.5mm] (C5) at (300:1.5cm) {};
+      \node[charge, negative, xshift= 2.5mm] (C6) at (360:1.5cm) {};
 
       \draw[white] (C1) to (C2) to (C3) to (C4) to (C5) to (C6) to (C1);
       % \draw[gray, dashed] (C2) to (C4) to (C6) to (C2);
 
-      \draw[orange, very thick, <-] (C6) to ++(.7,0);
-      \draw[orange, very thick, <-] (C3) to ++(-.7,0);
+      \foreach \d in {C1, C2} {
+        \draw[orange, very thick, <-] (\d) to ++(0,.7);
+      }
+
+      \foreach \d in {C4, C5} {
+        \draw[orange, very thick, <-] (\d) to ++(0,-.7);
+      }
 
       \node[white] (E) {\(\vec{E}_p\)};
       \begin{scope}[node distance = .5mm]
@@ -761,8 +769,9 @@
       % \draw[gray, thick, dotted] (E) to ++(0,2);
       % \draw[gray, thick, dotted] (E) to ++(0,-2);
     \end{scope}
-    \pause
+	\pause
 
+	%% square with vertical pressure 
     \begin{scope}[yshift=-4.5cm]
       \matrix[nodes = { charge }, row sep = 5mm, column sep = 1cm] {
         \node[positive] (NW) {}; & \node[negative] (N) {}; & \node [positive] (NE) {}; \\
@@ -782,33 +791,32 @@
     \end{scope}
     \pause
 
+	%% hex with horizontal pressure
     \begin{scope}[xshift=5.5cm, yshift=-4.5cm]
-      \node[charge, positive, yshift=-2.5mm] (C1) at ( 60:1.5cm) {};
-      \node[charge, negative, yshift=-2.5mm] (C2) at (120:1.5cm) {};
-      \node[charge, positive, xshift=-2.5mm] (C3) at (180:1.5cm) {};
-      \node[charge, negative, yshift= 2.5mm] (C4) at (240:1.5cm) {};
-      \node[charge, positive, yshift= 2.5mm] (C5) at (300:1.5cm) {};
-      \node[charge, negative, xshift= 2.5mm] (C6) at (360:1.5cm) {};
+      \node[charge, positive, yshift= 2.5mm] (C1) at ( 60:1.5cm) {};
+      \node[charge, negative, yshift= 2.5mm] (C2) at (120:1.5cm) {};
+      \node[charge, positive, xshift= 2.5mm] (C3) at (180:1.5cm) {};
+      \node[charge, negative, yshift=-2.5mm] (C4) at (240:1.5cm) {};
+      \node[charge, positive, yshift=-2.5mm] (C5) at (300:1.5cm) {};
+      \node[charge, negative, xshift=-2.5mm] (C6) at (360:1.5cm) {};
 
       \draw[white] (C1) to (C2) to (C3) to (C4) to (C5) to (C6) to (C1);
       % \draw[gray, dashed] (C2) to (C4) to (C6) to (C2);
 
-      \foreach \d in {C1, C2} {
-        \draw[orange, very thick, <-] (\d) to ++(0,.7);
-      }
-
-      \foreach \d in {C4, C5} {
-        \draw[orange, very thick, <-] (\d) to ++(0,-.7);
-      }
+      \draw[orange, very thick, <-] (C6) to ++(.7,0);
+      \draw[orange, very thick, <-] (C3) to ++(-.7,0);
 
       \node[white] (E) {\(\vec{E}_p\)};
       \begin{scope}[node distance = .5mm]
-        \node[red!50, right = of E] {\(+\)};
-        \node[blue!50, left = of E] {\(-\)};
+        \node[blue!50, right = of E] {\(-\)};
+        \node[red!50, left = of E] {\(+\)};
       \end{scope}
       % \draw[gray, thick, dotted] (E) to ++(0,2);
       % \draw[gray, thick, dotted] (E) to ++(0,-2);
     \end{scope}
+    \pause
+	  
+
   \end{tikzpicture}
 \end{frame}
 
@@ -816,22 +824,11 @@
   \frametitle{Licht in Kristallen}
   \begin{columns}[T]
     \begin{column}{.5\textwidth}
-      Symmetriegruppe und Darstellung
-      \begin{align*}
-        G &= \left\{\mathbb{1}, r, \sigma, \dots \right\} \\
-        &\Phi : G \to O(n)
-      \end{align*}
-      \begin{align*}
-        U_\lambda &= \left\{ v : \Phi v = \lambda v \right\} \\
-        &= \mathrm{null}\left(\Phi - \lambda I\right)
-      \end{align*}
       Helmholtz Wellengleichung
       \[
         \nabla^2 \vec{E} = \ten{\varepsilon}\mu
         \frac{\partial^2}{\partial t^2} \vec{E}
       \]
-    \end{column}
-    \begin{column}{.5\textwidth}
       Ebene Welle
       \[
         \vec{E} = \vec{E}_0 \exp\left[i
@@ -841,9 +838,17 @@
       \[
         (\ten{K}\ten{\varepsilon})\vec{E} = \frac{k^2}{\mu \omega^2} \vec{E}
       \]
-      \[
-        \vec{E} \in U_\lambda \implies (\ten{K}\ten{\varepsilon}) \vec{E} = \lambda \vec{E}
-      \]
+    \end{column}
+    \begin{column}{.5\textwidth}
+      Symmetriegruppe und Darstellung
+      \begin{align*}
+        G &= \left\{\mathbb{1}, r, \sigma, \dots \right\} \\
+        &\Phi : G \to O(n)
+      \end{align*}
+      \begin{align*}
+        U_\lambda &= \left\{ v : \Phi v = \lambda v \right\} \\
+        &= \mathrm{null}\left(\Phi - \lambda I\right)
+      \end{align*}
     \end{column}
   \end{columns}
 }
-- 
cgit v1.2.1


From 941187a21b3ff980e2dc742e13108f066822cdfa Mon Sep 17 00:00:00 2001
From: tim30b <tim.toenz@ost.ch>
Date: Sun, 9 May 2021 17:30:54 +0200
Subject: git will das ich commite

---
 vorlesungen/punktgruppen/slides.tex | 91 ++++++++++++++++++++++++++-----------
 1 file changed, 65 insertions(+), 26 deletions(-)

(limited to 'vorlesungen/punktgruppen/slides.tex')

diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
index e15dd9a..5e12fa9 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -6,6 +6,8 @@
 
 % pretty drawings
 \usepackage{tikz}
+\usepackage{tikz-3dplot}
+
 \usetikzlibrary{positioning}
 \usetikzlibrary{arrows.meta}
 \usetikzlibrary{shapes.misc}
@@ -83,7 +85,7 @@
   \begin{itemize}
     \item Was heisst \emph{Symmetrie} in der Mathematik? \pause
     \item Wie kann ein Kristall modelliert werden? \pause
-    \item Aus der Physik: Piezoelektrizit\"at \pause
+    \item Aus der Physik: Licht, Piezoelektrizit\"at \pause
   \end{itemize}
   \begin{center}
     \begin{tikzpicture}
@@ -823,34 +825,71 @@
 \frame{
   \frametitle{Licht in Kristallen}
   \begin{columns}[T]
-    \begin{column}{.5\textwidth}
-      Helmholtz Wellengleichung
-      \[
-        \nabla^2 \vec{E} = \ten{\varepsilon}\mu
-        \frac{\partial^2}{\partial t^2} \vec{E}
-      \]
-      Ebene Welle
-      \[
-        \vec{E} = \vec{E}_0 \exp\left[i
-          \left(\vec{k}\cdot\vec{r} - \omega t \right)\right]
-      \]
-      Anisotropisch Dielektrikum
-      \[
-        (\ten{K}\ten{\varepsilon})\vec{E} = \frac{k^2}{\mu \omega^2} \vec{E}
-      \]
+    \begin{column}{.45\textwidth}
+      \onslide<2->{
+        Helmholtz Wellengleichung
+        \[
+          \nabla^2 \vec{E} = \ten{\varepsilon}\mu
+          \frac{\partial^2}{\partial t^2} \vec{E}
+        \]
+      }
+      \onslide<3->{
+        Ebene Welle
+        \[
+          \vec{E} = \vec{E}_0 \exp\left[i
+            \left(\vec{k}\cdot\vec{r} - \omega t \right)\right]
+        \]
+      }
+      \onslide<4->{
+        Anisotropisch Dielektrikum
+        \[
+          (\ten{K}\ten{\varepsilon})\vec{E} 
+            = \frac{k^2}{\mu \omega^2} \vec{E}
+          \implies
+          \Phi \vec{E} = \lambda \vec{E}
+        \]
+      }
     \end{column}
-    \begin{column}{.5\textwidth}
-      Symmetriegruppe und Darstellung
-      \begin{align*}
-        G &= \left\{\mathbb{1}, r, \sigma, \dots \right\} \\
-        &\Phi : G \to O(n)
-      \end{align*}
-      \begin{align*}
-        U_\lambda &= \left\{ v : \Phi v = \lambda v \right\} \\
-        &= \mathrm{null}\left(\Phi - \lambda I\right)
-      \end{align*}
+    \begin{column}{.55\textwidth}
+      \onslide<5->{
+        Eingenraum
+        \begin{align*}
+          U_\lambda &= \left\{ v : \Phi v = \lambda v \right\}
+          = \mathrm{null}\left(\Phi - \lambda I\right)
+        \end{align*}
+      }\onslide<6->{
+        Symmetriegruppe und Darstellung
+        \begin{align*}
+          G &= \left\{\mathbb{1}, r, \sigma, \dots \right\} \\
+          &\Phi : G \to O(n)
+        \end{align*}
+      }\onslide<7->{
+        Kann man \(U_\lambda\) von \(G\) herauslesen?
+        \only<7>{
+          \[
+            U_\lambda \stackrel{?}{=} f\left(\bigoplus_{g \in G} \Phi_g\right)
+          \]
+        }\only<8>{
+          \begin{align*}
+            \mathrm{Tr}\left[\Phi_r(g)\right] 
+              &= \sum_i n_i \mathrm{Tr}\left[\Psi_i(g)\right] \\
+            |G| &= \sum_i\mathrm{Tr}\left[\Psi_i(\mathbb{1})\right]
+          \end{align*}
+        }
+      }
     \end{column}
   \end{columns}
 }
 
+% \begin{frame}[fragile]
+%   \centering
+%   \tdplotsetmaincoords{70}{110}
+%   \begin{tikzpicture}[scale=2, tdplot_main_coords]
+%     \node[draw=white, thick, minimum size = 3cm, circle] {};
+%     % \foreach \x in {0, 120, 240} {
+%     % }
+%   \end{tikzpicture}
+% \end{frame}
+
+
 \end{document}
-- 
cgit v1.2.1


From dbeaa2f31d51c098caf46b83ca286cbef358f996 Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Mon, 10 May 2021 13:14:42 +0200
Subject: Recompile slides for handout

---
 vorlesungen/punktgruppen/slides.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

(limited to 'vorlesungen/punktgruppen/slides.tex')

diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
index 5e12fa9..cd3d7d7 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -1,4 +1,4 @@
-\documentclass[12pt, xcolor, aspectratio=169]{beamer}
+\documentclass[12pt, xcolor, aspectratio=169, handout]{beamer}
 
 % language
 \usepackage{polyglossia}
-- 
cgit v1.2.1

