updated tutorial 6 + added gnu plot save file

[lectures/latex.git] / solid_state_physics / tutorial / 1_06s.tex

diff --git a/solid_state_physics/tutorial/1_06s.tex b/solid_state_physics/tutorial/1_06s.tex
index 4e965e3..7d55113 100644 (file)
--- a/solid_state_physics/tutorial/1_06s.tex
+++ b/solid_state_physics/tutorial/1_06s.tex
@@ -16,6 +16,8 @@
 \usepackage{pstricks}
 \usepackage{pst-node}
 \usepackage{rotating}
+\usepackage{epic}
+\usepackage{eepic}
 
 \setlength{\headheight}{0mm} \setlength{\headsep}{0mm}
 \setlength{\topskip}{-10mm} \setlength{\textwidth}{17cm}
@@ -66,13 +68,34 @@
        \end{itemize}
 \end{enumerate}
 
-\section{\ldots}
-
-\ldots
+\section{Dielectric function of the free electron gas}
 
 \begin{enumerate}
- \item \ldots
- \item \ldots
+ \item \begin{itemize}
+        \item Equation of motion: $m\frac{d^2x}{dt^2}=-eE$
+       \item Ansatz: $x(t)=x_0 e^{-i\omega t}$
+        \item Solution of the equation of motion: $-m\omega^2x=-eE$
+        \item Dipole moment: $p=-ex=\frac{-e^2E}{m\omega^2}$
+        \item Polarization: $P=np=\frac{-ne^2E}{m\omega^2}$
+       \item Dielectric function:
+             $\epsilon(\omega)=1+\frac{P}{\epsilon_0E}
+                              =1+\frac{-ne^2E}{m\omega^2\epsilon_0E}
+                              =1-\frac{ne^2}{\epsilon_0m\omega^2}$
+       \end{itemize}
+ \item \begin{itemize}
+        \item Using $\omega_p^2=\frac{ne^2}{\epsilon_0m}$\\
+             $\Rightarrow \epsilon(\omega)=1-\frac{\omega_p^2}{\omega^2}$
+        \item Sketch of dielectric function:\\
+              (page 2)
+        \item Influence on electromagnetic waves:\\
+             $\frac{\omega}{\omega_p}>1\Leftrightarrow \omega>\omega_p$:
+              $\Rightarrow \epsilon=n^2>0$
+             $\Rightarrow$ transparent region\\
+             $\frac{\omega}{\omega_p}<1\Leftrightarrow \omega<\omega_p$:
+              $\Rightarrow \epsilon=n^2<0$
+             $\Rightarrow$ reflective region\\
+       \end{itemize}
+\input{dielectric_pslatex}
 \end{enumerate}
 
 \end{document}