# Thomas–Fermi Model - Total Energy

Total Energy

The total energy of the electrons is the sum of their kinetic and potential energies,

\begin{align} E & = T \ + \ U_{eN} \ + \ U_{ee} \\ & = C_F\int ^{5/3}\ d^3r \ + \int n(\vec{r}) \ V_N(\vec{r}) \ d^3r \ + \ \frac{1}{2} \ e^2 \int \frac{n(\vec{r}) \ n(\vec{r} \, ')} {\left\vert \vec{r} - \vec{r} \, ' \right\vert } \ d^3r \ d^3r' \\ \end{align}

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