From: hackbard Date: Thu, 13 Dec 2007 13:30:07 +0000 (+0100) Subject: 1_02s final X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=9cec2b7c91613a9f723957731b444e5b97211ce4;p=lectures%2Flatex.git 1_02s final --- diff --git a/solid_state_physics/tutorial/1_02s.tex b/solid_state_physics/tutorial/1_02s.tex index 6f08cae..ccb4a26 100644 --- a/solid_state_physics/tutorial/1_02s.tex +++ b/solid_state_physics/tutorial/1_02s.tex @@ -152,7 +152,8 @@ &=&C\left(\frac{1}{M_1}+\frac{1}{M_2}\right)\pm \sqrt{C^2\frac{(M_1+M_2)^2}{M_1^2M_2^2}- \frac{1}{M_1M_2}2C^2(1-cos(ka))} \nonumber \\ - &=&C\left(\frac{1}{M_1}+\frac{1}{M_2}\right)\pm + &=&C\left(\frac{1}{M_1}+\frac{1}{M_2}\right) + \stackrel{{\color{red}+}}{{\color{blue}-}} C\sqrt{\left(\frac{1}{M_1}+\frac{1}{M_2}\right)^2- \frac{2(1-\cos(ka))}{M_1M_2}} \nonumber \end{eqnarray} @@ -217,8 +218,8 @@ Acoustic branch: $\omega^2\approx \frac{C/2}{M_1+M_2}k^2a^2$\\ \item $k=0$:\\ - Optical branch: $u/v = - M_2/M_1$ (out of phase)\\ - \item $k=\pm \pi/a$:\\ + $\rightarrow u/v = - M_2/M_1$ (out of phase)\\ + \item $k=\pi/a$\\ $\rightarrow \omega^2=2C/M_2,2C/M_1$ \end{itemize} \end{enumerate}