From: hackbard Date: Wed, 9 Jan 2008 15:41:39 +0000 (+0100) Subject: item symbol was misleading! X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=c5abf796bf194d6130745d8f33cfc3fffe62ef33;p=lectures%2Flatex.git item symbol was misleading! --- diff --git a/solid_state_physics/tutorial/1_05s.tex b/solid_state_physics/tutorial/1_05s.tex index 77a03e6..d33f033 100644 --- 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 $dZ$:\\ + $\frac{dE}{dk}=\frac{\hbar^2}{m}k \rightarrow + dk=\frac{m}{\hbar^2k}dE$\\ + $k=\frac{\sqrt{2m}}{\hbar^2}\sqrt{E}$\\ $\Rightarrow dZ'=\frac{4\pi k^2m}{(\pi/L)^3\hbar^2k} dE= \frac{4\pi\frac{\sqrt{2m}}{\hbar}\sqrt{E}m}{8(\pi/L)^3\hbar^2}dE =\frac{(2m)^{3/2}L^3}{4\pi^2\hbar^3}\sqrt{E}dE$\\