fixes + tutorial 4

[lectures/latex.git] / solid_state_physics / tutorial / 1_04s.tex

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+\pdfoutput=0
+\documentclass[a4paper,11pt]{article}
+\usepackage[activate]{pdfcprot}
+\usepackage{verbatim}
+\usepackage{a4}
+\usepackage{a4wide}
+\usepackage[german]{babel}
+\usepackage[latin1]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{amsmath}
+\usepackage{ae}
+\usepackage{aecompl}
+\usepackage[dvips]{graphicx}
+\graphicspath{{./img/}}
+\usepackage{color}
+\usepackage{pstricks}
+\usepackage{pst-node}
+\usepackage{rotating}
+
+\setlength{\headheight}{0mm} \setlength{\headsep}{0mm}
+\setlength{\topskip}{-10mm} \setlength{\textwidth}{17cm}
+\setlength{\oddsidemargin}{-10mm}
+\setlength{\evensidemargin}{-10mm} \setlength{\topmargin}{-1cm}
+\setlength{\textheight}{26cm} \setlength{\headsep}{0cm}
+
+\renewcommand{\labelenumi}{(\alph{enumi})}
+
+\begin{document}
+
+% header
+\begin{center}
+ {\LARGE {\bf Materials Physics I}\\}
+ \vspace{8pt}
+ Prof. B. Stritzker\\
+ WS 2007/08\\
+ \vspace{8pt}
+ {\Large\bf Tutorial 4 - proposed solutions}
+\end{center}
+
+\section{Hall effect and magnetoresistance}
+\begin{enumerate}
+ \item \begin{itemize}
+        \item probability: $1-\frac{dt}{\tau}$
+       \item momentum contribution of non-colliding electrons:
+             $f(t)dt+O(dt)^2$
+        \item momentum per electron at time $t+dt$:\\
+             \[
+             p(t+dt)=\left(1-\frac{dt}{\tau}\right)
+                     \left[p(t)+f(t)dt+O(dt)^2\right]
+                    =p(t)-\frac{dt}{\tau}p(t)+f(t)+O(dt)^2
+             \]
+       \end{itemize}
+ \item \[
+       p(t+dt)-p(t)=-\frac{dt}{\tau}p(t)+f(t)dt+O(dt)^2
+       \]
+       \[
+       \frac{p(t+dt)-p(t)}{dt}=-\frac{p(t)}{\tau}+f(t)+\frac{O(dt)^2}{dt}
+       \]
+       \[
+       \stackrel{dt\rightarrow 0}{\Rightarrow} \quad
+       \frac{dp(t)}{dt}=-\frac{p(t)}{\tau}+f(t)
+       \]
+ \item
+\end{enumerate}
+
+\end{document}