deletions | additions       diff --git a/The_integer_QHE_has_a__.tex b/The_integer_QHE_has_a__.tex  index f3c04c1..5c80568 100644  --- a/The_integer_QHE_has_a__.tex  +++ b/The_integer_QHE_has_a__.tex 
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\textit{I}_x\sim\langle{u_k}|\frac{\partial{H(k(t))}}{\partial{k_x}}|u_k\rangle  =\partial_x\textit{E}_k-\langle{\partial_x{u_k}}|\textit{H(k)}|u_k\rangle-\langle{u_k}|\textit{H(k)}|\partial_x{u_k}\rangle  \end{equation}  where $\partial_x=\frac{\partial}{\partial{k_x}}$. With Schrodinger's equation  \begin{equation}  \textit{H(k)}|u_k\rangle=  \end{equation}