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I am reading a textbook on many-electron theory, which gives a Bloch equation in its generalized form: $$\tag{1} [\Omega,H_0]P=Q(V\Omega-\Omega V_{eff})P,$$ where $P$ denotes the projection from exact state to a model state: $$\tag{2} P\mid \psi^{(\alpha)}\rangle=\mid \psi_0^{(\alpha)}\rangle, ... 12:46 AM 6 If the GGA xc energy is defined as$$ E_{xc}[n] = \int n(\mathbf{r}) \varepsilon_{xc}[n(\mathbf{r}), \nabla n(\mathbf{r})]\ d\mathbf{r}, $$the potential can be written as$$ V_{xc}[n] = \varepsilon_{xc} + n\frac{\partial \varepsilon_{xc}}{\partial n} - \nabla\cdot\left[n\frac{\partial \varepsilo...