Physical-quantities.md

@@ -3,7 +3,7 @@
 # Energy
 Energy is computed from the formula:
 ```math
-E=\int \mathcal{E}_{\textrm{edf}}(n,\nu,\ldots)\,d^3r+\sum_{\sigma}\int V_{\sigma}^{\textrm{(ext)}}(r)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
+E=\int \mathcal{E}_{\textrm{edf}}(n,\nu,\ldots)\,d^3r+\sum_{\sigma}\int V_{\sigma}^{\textrm{(ext)}}(r)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
 ```  
 
 The instrictic energy is assumed to have the generic structure:
@@ -34,7 +34,7 @@ E_{\textrm{pot.ext}} = \int \sum_{\sigma=\{\uparrow,\downarrow\}} V_{\sigma}^{\t
 ```
 * `E_pairext`:
 ```math
-E_{\textrm{pair.ext}} = -\int\left(\Delta^{\textrm{(ext)}}(r)\nu^*(r)+\textrm{h.c.}\right)d^3r
+E_{\textrm{pair.ext}} = -\frac{1}{2}\int\left(\Delta^{\textrm{(ext)}}(r)\nu^*(r)+\textrm{h.c.}\right)d^3r
 ```
 * `E_velext`:
 ```math