the mpi publication, finally!

[lectures/latex.git] / solid_state_physics / tutorial / 1_05s.tex

diff --git a/solid_state_physics/tutorial/1_05s.tex b/solid_state_physics/tutorial/1_05s.tex
index 77a03e6..d33f033 100644 (file)
--- a/solid_state_physics/tutorial/1_05s.tex
+++ b/solid_state_physics/tutorial/1_05s.tex
@@ -55,12 +55,10 @@
                      \approx 4\pi k^2dk$
              \end{itemize}
              $\Rightarrow dZ'=\frac{\frac{1}{8}4\pi k^2dk}{(\pi/L)^3}$
-        \item Express $dk$ and $k$ by $dE$ and $E$ and insert it into $dZ$:
-              \begin{itemize}
-               \item $\frac{dE}{dk}=\frac{\hbar^2}{m}k \rightarrow
-                     dk=\frac{m}{\hbar^2k}dE$
-               \item $k=\frac{\sqrt{2m}}{\hbar^2}\sqrt{E}$
-             \end{itemize}
+        \item Express $dk$ and $k$ by $dE$ and $E$ and insert it into $dZ$:\\
+              $\frac{dE}{dk}=\frac{\hbar^2}{m}k \rightarrow
+              dk=\frac{m}{\hbar^2k}dE$\\
+              $k=\frac{\sqrt{2m}}{\hbar^2}\sqrt{E}$\\
              $\Rightarrow dZ'=\frac{4\pi k^2m}{(\pi/L)^3\hbar^2k} dE=
               \frac{4\pi\frac{\sqrt{2m}}{\hbar}\sqrt{E}m}{8(\pi/L)^3\hbar^2}dE
               =\frac{(2m)^{3/2}L^3}{4\pi^2\hbar^3}\sqrt{E}dE$\\