deletions | additions       diff --git a/Magnetic response.tex b/Magnetic response.tex  index 8978b28..f76fc15 100644  --- a/Magnetic response.tex  +++ b/Magnetic response.tex 
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%  \begin{equation}  \label{eq:hypervirial}  i\langle\varphi_j\vert{\hat\vec{p}}\vert\varphi_n\rangle i\langle\varphi_j\vert{\hat{\vec{p}}}\vert\varphi_n\rangle  = (\epsilon_n-\epsilon_j)\langle\varphi_j\vert{\hat\vec{r}}\vert\varphi_n\rangle\ (\epsilon_n-\epsilon_j)\langle\varphi_j\vert{\hat{\vec{r}}}\vert\varphi_n\rangle\  , \end{equation}  where \(\epsilon_n\) is the eigenvalue of the state \(\varphi_n\). 
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\begin{equation}  \label{eq:hypervirial_nl}  i\langle\varphi_j\vert\hat{\vec{p}}\vert\varphi_n\rangle =   (\epsilon_n-\epsilon_j)\langle\varphi_j\vert\hat\vec{r}\vert\varphi_n\rangle (\epsilon_n-\epsilon_j)\langle\varphi_j\vert\hat{\vec{r}}\vert\varphi_n\rangle  + \langle\varphi_j\vert[\hat\vec{r},\hat v_{\text{nl}}]\vert\varphi_n\rangle\ \langle\varphi_j\vert[\hat{\vec{r}},\hat{v}_{\text{nl}}]\vert\varphi_n\rangle\  . \end{equation}  %