X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=solid_state_physics%2Ftutorial%2F2_01s.tex;h=033c8ae2702dfe6cab0e232e27b839759de98d33;hp=a89285334154eae2075e616659fcb51e12e032eb;hb=183bd2b78445842ee859e2f10f8ab9dc84cf2776;hpb=a548ec888564c4aca659f187c41f3f995842a7f6

diff --git a/solid_state_physics/tutorial/2_01s.tex b/solid_state_physics/tutorial/2_01s.tex
index a892853..033c8ae 100644
--- a/solid_state_physics/tutorial/2_01s.tex
+++ b/solid_state_physics/tutorial/2_01s.tex
@@ -62,7 +62,7 @@
         \item $I = (\textrm{charge}) \cdot (\textrm{loops per time})
 	       \stackrel{1/T=\omega_L/2\pi}{=}
 	       (Ze)(\frac{1}{2\pi}\frac{-e}{2m}B)$\\
-	      $\mu=IA=I2\pi<\rho^2>=-\frac{Ze^2B}{4m}<\rho^2>$\\
+	      $\mu=IA=I\pi<\rho^2>=-\frac{Ze^2B}{4m}<\rho^2>$\\
 	      $<x^2>=<y^2>=<z^2> \Rightarrow <r^2>=3<x^2>=3<y^2>$\\
 	      $<\rho^2>=<x^2>+<y^2>=\frac{2}{3}<r^2>$\\
 	      $\mu=-\frac{Ze^2B}{6m}$
@@ -92,18 +92,18 @@
 	       \left(0,0,B\right)$\\
 	      Note: $\nabla_r{\bf A}=0$
         \item $
-	      H_{kin}'=\frac{i\hbar e}{2m}\left(
+	      H_{kin}'=\frac{i\hbar e}{2m}\frac{B}{2}\left(
 	       x\frac{\partial}{\partial y}-y\frac{\partial}{\partial x}
 	                                  \right)+\frac{e^2B^2}{8m}(x^2+y^2)
 	      $\\
 	      $
 	       L_z=x\frac{\partial}{\partial y}-y\frac{\partial}{\partial x}
-	       \Rightarrow  H_{kin}'=\frac{i\hbar e}{2m}L_z+
+	       \Rightarrow  H_{kin}'=\frac{i\hbar e}{2m}\frac{B}{2}L_z+
 	       \frac{e^2B^2}{8m}(x^2+y^2)
 	      $
         \item $\chi=-\frac{1}{V}\mu_0\frac{\partial^2 E}{\partial B^2}
 	       \Rightarrow$
-	      only second term contributes to $\chi$!
+	      only second term contributes to $\chi$!\\
 	      $\chi=-\frac{1}{V}\mu_0\frac{e^2}{4m}<\phi|(x^2+y^2)|\phi>$
 	\item $<\phi|x^2|\phi>=<\phi|y^2|\phi>=\frac{1}{3}<\phi|r^2|\phi>$\\
 	      $\Rightarrow \chi=-\frac{1}{V}\mu_0\frac{e^2}{6m}