From 9cec2b7c91613a9f723957731b444e5b97211ce4 Mon Sep 17 00:00:00 2001
From: hackbard <hackbard@sage.physik.uni-augsburg.de>
Date: Thu, 13 Dec 2007 14:30:07 +0100
Subject: [PATCH] 1_02s final
---
solid_state_physics/tutorial/1_02s.tex | 7 ++++---
1 file changed, 4 insertions(+), 3 deletions(-)
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}
--
2.39.5