External-potentials.md

 # Form of the functional
 W-SLDA codes minimize functional of the generic form:  
 ```math
-E=\int \mathcal{E}_{\textrm{edf}}(n,\nu,\ldots)\,d^3r-\sum_{\sigma}\int\left(\mu_{\sigma}-V_{\sigma}^{\textrm{(ext)}}(r)\right)n_{\sigma}(r)\,d^3r\\-\frac{1}{2}\int\left(\Delta^{\textrm{(ext)}}(r)\nu^*(r)+\textrm{h.c.}\right)d^3r-\sum_{\sigma}\int \vec{v}_{\sigma}^{\textrm{(ext)}}(r)\cdot\vec{j}_{\sigma}(r)\,d^3r
+E=\int \mathcal{E}_{\textrm{edf}}(n,\nu,\ldots)\,d^3r-\sum_{\sigma}\int\left(\mu_{\sigma}-V_{\sigma}^{\textrm{(ext)}}(r)\right)n_{\sigma}(r)\,d^3r\\-\int\left(\Delta^{\textrm{(ext)}}(r)\nu^*(r)+\textrm{h.c.}\right)d^3r-\sum_{\sigma}\int \vec{v}_{\sigma}^{\textrm{(ext)}}(r)\cdot\vec{j}_{\sigma}(r)\,d^3r
 ``` 
 where:  
 * $`\mathcal{E}_{\textrm{edf}}(n,\nu,\ldots)`$ is energy density functional which defines the physical system,