bugfix in 1_01s + changed excercise in 1_02

diff --git a/solid_state_physics/tutorial/1_01s.tex b/solid_state_physics/tutorial/1_01s.tex
index 83391bb..ef49e3c 100644 (file)
--- a/solid_state_physics/tutorial/1_01s.tex
+++ b/solid_state_physics/tutorial/1_01s.tex
@@ -79,7 +79,7 @@
          \[
          - \frac{\hbar^2}{2m} \frac{d^2}{dx^2} F_x(x) = E_x F_x(x), \quad
          - \frac{\hbar^2}{2m} \frac{d^2}{dy^2} F_y(y) = E_y F_y(y),\quad
-         - \frac{\hbar^2}{2m} \frac{d^2}{dz^2} F_z(z) = E_x F_z(z).
+         - \frac{\hbar^2}{2m} \frac{d^2}{dz^2} F_z(z) = E_z F_z(z).
         \]
         \[
          \Rightarrow \Big[E_x + E_y + E_z\Big] F_x(x) F_y(y) F_z(z) =

diff --git a/solid_state_physics/tutorial/1_02.tex b/solid_state_physics/tutorial/1_02.tex
index 55733e6..a96368f 100644 (file)
--- a/solid_state_physics/tutorial/1_02.tex
+++ b/solid_state_physics/tutorial/1_02.tex
@@ -37,27 +37,7 @@
  {\Large\bf Tutorial 2}
 \end{center}
 
-\section{Band structure: indirect band gap of silicon}
-Some facts about silicon:
-\begin{itemize}
- \item Lattice constant: $a=5.43 \times 10^{-10} \, m$.
- \item Silicon has an indirect band gap.
-       \begin{itemize}
-        \item The minimum of the conduction band is located at
-             $k=0.85 \frac{2 \pi}{a}$.
-       \item The maximum of the valance band is located at $k=0$.
-       \item The energy gap is $E_g=1.12 \, eV$.
-       \end{itemize}
-\end{itemize}
-\begin{enumerate}
- \item Calculate the wavelength of the light necessary to lift an electron from
-       the valence to the conduction band.
-       What is the momentum of such a photon?
- \item Calculate the phonon momentum necessary for the transition.
-       Compare the momentum values of phonon and photon.
-\end{enumerate}
-
-\section{Phonons}
+\section{Phonons 1}
 Consider two masses $M_1$ and $M_2$ with their idle positions
 $r_{10}$ and $r_{20}$ connected by a spring with spring constant $D$.
 The equilibrium distance vector is $\rho_{0}=r_{20}-r_{10}$.
@@ -90,4 +70,11 @@ The vector of elongation is thus given by $\sigma = u_2 -u_1$.
        keeping earlier results in mind.
 \end{enumerate}
 
+\section{Phonons 2}
+\begin{enumerate}
+\item Derive the dispersion relation for a linear chain with two different
+      alternating types of atoms.
+\item Discuss the two solutions for $\omega^2$.
+\end{enumerate}
+
 \end{document}