deletions | additions       diff --git a/Magnetic response.tex b/Magnetic response.tex  index 70c03d2..1c57072 100644  --- a/Magnetic response.tex  +++ b/Magnetic response.tex 
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\begin{equation}  \label{eq:magneticmoment}  \vec{m}^0=  \sum_k\bra{\varphi_k}\delta{\vec{V}}^{\mathrm{mag}}\ket{\varphi_{k}}\ \sum_k\langle\varphi_k|\delta{\vec{V}}^{\mathrm{mag}}|\varphi_{k}\rangle\  . \end{equation}  %  For the susceptibility, we need to calculate the first order response