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Time Dependent Kohn-Sham Equation

$$i \hbar \frac{\partial}{\partial t} u_{n, k} = \left[ \frac{1}{2m} \left( {p}^2 + \frac{e}{c}{{A}} \right) + V_\mathrm{H} + V_\mathrm{XC} + V_\mathrm{nucl} \right] u_{n,k}$$

- $$u_{nk}(\mathbf{r},t)$$ is the Kohn-Sham orbital of the band index $$n$$ .

- $$A$$ is the vector potential.

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