checkin for sync to d81

[lectures/latex.git] / solid_state_physics / tutorial / 2n_01.tex

diff --git a/solid_state_physics/tutorial/2n_01.tex b/solid_state_physics/tutorial/2n_01.tex
index b53a276..404988f 100644 (file)
--- a/solid_state_physics/tutorial/2n_01.tex
+++ b/solid_state_physics/tutorial/2n_01.tex
@@ -68,6 +68,6 @@ The parabolic approximation of the density of states of electrons in the conduct
 $D_c(\epsilon)=\frac{1}{2\pi^2}(\frac{2m_n}{\hbar^2})^{3/2}(\epsilon-E_c)^{1/2}$ and
 $D_v(\epsilon)=\frac{1}{2\pi^2}(\frac{2m_p}{\hbar^2})^{3/2}(E_v-\epsilon)^{1/2}$.
 Simplify the Fermi function before calculating the integral and use the substitutions $x=(\epsilon - E_{\text{c}})/k_{\text{B}}T$ and $x=(E_{\text{v}}-\epsilon)/k_{\text{B}}T$.
-Furthermore use the equality $\int_0^{\infty} x^{1/2} e^{-x} dx = 1/2 \sqrt{\pi}$.
+Furthermore use the equality $\int_0^{\infty} x^{1/2} e^{-x} dx = \frac{\sqrt{\pi}}{2}$.
 
 \end{document}