deletions | additions       diff --git a/The_integer_QHE_has_a__.tex b/The_integer_QHE_has_a__.tex  index f6c9ed3..777239d 100644  --- a/The_integer_QHE_has_a__.tex  +++ b/The_integer_QHE_has_a__.tex 
...
\textit{H(k)}|u_k\rangle=i \frac{\partial}{\partial{t}}|u_k\rangle=i (\dot{k_x}\partial_x+\dot{k_y}\partial_y)|u_k\rangle  \end{equation}  \begin{equation}  \textit{I}_x\sim\partial_x\textit{E_{k}}-b_{z}(k)\dot{k_y} \textit{I}_x\sim\partial_x\textit{E}_{k}-b_{z}(k)\dot{k_y}  \end{equation}  \begin{equation}  b_z(k)=i(\langle\partial_x{u_k}|\partial_y{u_k}\rangle-\langle\partial_y{u_k}|\partial_x{u_k}\rangle)