  We present a method to calculate the electronic charge density of periodic
solids in the GW approximation, using the space-time method. We investigate for
the examples of silicon and germanium to what extent the GW approximation is
charge-conserving and how the charge density compares with experimental values.
We find that the GW charge density is close to experiment and charge is
practically conserved. We also discuss how using a Hartree potential consistent
with the level of approximation affects the quasi-particle energies and find
that the common simplification of using the LDA Hartree potential is a very
well justified.
