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32 {\LARGE {\bf Materials Physics I}\\}
37 {\Large\bf Tutorial 4 - proposed solutions}
40 \section{Hall effect and magnetoresistance}
43 \item probability: $1-\frac{dt}{\tau}$
44 \item momentum contribution of non-colliding electrons:
46 \item momentum per electron at time $t+dt$:\\
48 p(t+dt)=\left(1-\frac{dt}{\tau}\right)
49 \left[p(t)+f(t)dt+O(dt)^2\right]
50 =p(t)-\frac{dt}{\tau}p(t)+f(t)+O(dt)^2
54 p(t+dt)-p(t)=-\frac{dt}{\tau}p(t)+f(t)dt+O(dt)^2
57 \frac{p(t+dt)-p(t)}{dt}=-\frac{p(t)}{\tau}+f(t)+\frac{O(dt)^2}{dt}
60 \stackrel{dt\rightarrow 0}{\Rightarrow} \quad
61 \frac{dp(t)}{dt}=-\frac{p(t)}{\tau}+f(t)