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:
$$\tag{2}
P\mid \psi^{(\alpha)}\rangle=\mid \psi_0^{(\alpha)}\rangle,
$...
If the GGA xc energy is defined as
$$
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...
