From 6fe70c5cf84320a6a92167b678e76ef9448d713c Mon Sep 17 00:00:00 2001 From: hackbard Date: Mon, 12 Nov 2007 09:56:37 +0100 Subject: [PATCH] bugfix in 1_01s + changed excercise in 1_02 --- solid_state_physics/tutorial/1_01s.tex | 2 +- solid_state_physics/tutorial/1_02.tex | 29 +++++++------------------- 2 files changed, 9 insertions(+), 22 deletions(-) diff --git a/solid_state_physics/tutorial/1_01s.tex b/solid_state_physics/tutorial/1_01s.tex index 83391bb..ef49e3c 100644 --- 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 --- 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} -- 2.39.2