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Update Physical quantities authored by Gabriel Wlazłowski's avatar Gabriel Wlazłowski
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Physical-quantities.md
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...@@ -42,7 +42,7 @@ E_{\textrm{vel.ext}} = -\int \sum_{\sigma=\{\uparrow,\downarrow\}}\vec{v}_{\sigm ...@@ -42,7 +42,7 @@ E_{\textrm{vel.ext}} = -\int \sum_{\sigma=\{\uparrow,\downarrow\}}\vec{v}_{\sigm
The total energy `E_tot` is computed as the sum of all these contributions. The total energy `E_tot` is computed as the sum of all these contributions.
# Densities # Densities
Densities are computed according to formulas: Densities are computed according to formulas: (**TODO: there are missing ^2 in some formulas**)
* `nu`: * `nu`:
![\nu(r) = \frac{1}{2}\sum_{|E_n|<E_c} u_{n,\uparrow}(r)v_{n,\downarrow}^{*}(r)( f_{\beta}(-E_n)-f_{\beta}(E_n) )](https://render.githubusercontent.com/render/math?math=%5Cnu(r)%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Csum_%7B%7CE_n%7C%3CE_c%7D%20u_%7Bn%2C%5Cuparrow%7D(r)v_%7Bn%2C%5Cdownarrow%7D%5E%7B*%7D(r)(%20f_%7B%5Cbeta%7D(-E_n)-f_%7B%5Cbeta%7D(E_n)%20)) ![\nu(r) = \frac{1}{2}\sum_{|E_n|<E_c} u_{n,\uparrow}(r)v_{n,\downarrow}^{*}(r)( f_{\beta}(-E_n)-f_{\beta}(E_n) )](https://render.githubusercontent.com/render/math?math=%5Cnu(r)%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Csum_%7B%7CE_n%7C%3CE_c%7D%20u_%7Bn%2C%5Cuparrow%7D(r)v_%7Bn%2C%5Cdownarrow%7D%5E%7B*%7D(r)(%20f_%7B%5Cbeta%7D(-E_n)-f_%7B%5Cbeta%7D(E_n)%20))
* `rho_a`: * `rho_a`:
......