the mpi publication, finally!

[lectures/latex.git] / solid_state_physics / tutorial / 2_01s.tex

diff --git a/solid_state_physics/tutorial/2_01s.tex b/solid_state_physics/tutorial/2_01s.tex
index 5e23232..033c8ae 100644 (file)
--- a/solid_state_physics/tutorial/2_01s.tex
+++ b/solid_state_physics/tutorial/2_01s.tex
@@ -62,7 +62,7 @@
         \item $I = (\textrm{charge}) \cdot (\textrm{loops per time})
               \stackrel{1/T=\omega_L/2\pi}{=}
               (Ze)(\frac{1}{2\pi}\frac{-e}{2m}B)$\\
-             $\mu=IA=I2\pi<\rho^2>=-\frac{Ze^2B}{4m}<\rho^2>$\\
+             $\mu=IA=I\pi<\rho^2>=-\frac{Ze^2B}{4m}<\rho^2>$\\
              $<x^2>=<y^2>=<z^2> \Rightarrow <r^2>=3<x^2>=3<y^2>$\\
              $<\rho^2>=<x^2>+<y^2>=\frac{2}{3}<r^2>$\\
              $\mu=-\frac{Ze^2B}{6m}$
@@ -92,13 +92,13 @@
               \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}