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| -rw-r--r-- | vorlesungen/punktgruppen/slides.pdf | bin | 32512 -> 36038 bytes | |||
| -rw-r--r-- | vorlesungen/punktgruppen/slides.tex | 79 |
2 files changed, 73 insertions, 6 deletions
diff --git a/vorlesungen/punktgruppen/slides.pdf b/vorlesungen/punktgruppen/slides.pdf Binary files differindex d732296..bd7afc9 100644 --- a/vorlesungen/punktgruppen/slides.pdf +++ b/vorlesungen/punktgruppen/slides.pdf 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 \[ |