diff options
Diffstat (limited to 'vorlesungen/punktgruppen')
| -rw-r--r-- | vorlesungen/punktgruppen/slides.pdf | bin | 901496 -> 905022 bytes | |||
| -rw-r--r-- | vorlesungen/punktgruppen/slides.tex | 81 |
2 files changed, 43 insertions, 38 deletions
diff --git a/vorlesungen/punktgruppen/slides.pdf b/vorlesungen/punktgruppen/slides.pdf Binary files differindex 67c9f4a..2b2e0d8 100644 --- a/vorlesungen/punktgruppen/slides.pdf +++ b/vorlesungen/punktgruppen/slides.pdf 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} } |