deletions | additions       diff --git a/RDMFT1.tex b/RDMFT1.tex  index 6d416d2..ff73904 100644  --- a/RDMFT1.tex  +++ b/RDMFT1.tex 
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\begin{eqnarray}  \langle \phi_{i} | \phi_{j}\rangle = \delta_{ij}. \label{eqorth}  \end{eqnarray}  The bounds on the occupation numbers are automatically satisfied by setting $n_{i}=2\sin^2(2\pi\vartheta_i)$ and varying $\vartheta_{i}$ without constraints. The condition conditions  (\ref{eqsumocc}) is and (\ref{eqorth}) are  taken into account by using a via  Lagrange multiplyer multipliers  $\mu$ and Lagrange multiplyers $\lambda_{ik}$ are used for the orthonormality constraints (\ref{eqorth}). $\lambda_{ij}$, respectively.  Then, one can define the following functional \begin{eqnarray}  \Omega(N,\{\vartheta\} ,\{\phi_i(\mathbf{r})\})= E - \mu (\sum_i \left(\sum_{i=1}^\infty  2sin^2( 2\pi\vartheta_i)-N)-\sum_{ik} \lambda_{ik}(\langle\phi_k|\phi_i\rangle-\delta_{ki}) 2\pi\vartheta_i)-N\right)-\sum_{i,j=1}^\infty \lambda_{ij}(\langle\phi_i|\phi_j\rangle-\delta_{ij})  \end{eqnarray}  which has to be stationary with respect to variations in $\{\vartheta_i\}$, $\{\phi_i(\mathbf{r})\}$ and $\{\phi_i^{*}(\mathbf{r})\}$.  %\begin{eqnarray}