  We investigate the narrow-line region (NLR) of two radio-quiet QSOs,
PG1012+008 and PG1307+085, using high signal-to-noise spatially resolved
long-slit spectra obtained with FORS1 at the Very Large Telescope. Although the
emission is dominated by the point-spread function of the nuclear source, we
are able to detect extended NLR emission out to several kpc scales in both QSOs
by subtracting the scaled central spectrum from outer spectra. In contrast to
the nuclear spectrum, which shows a prominent blue wing and a broad line
profile of the [O III] line, the extended emission reveals no clear signs of
large scale outflows. Exploiting the wide wavelength range, we determine the
radial change of the gas properties in the NLR, i.e., gas temperature, density,
and ionization parameter, and compare them with those of Seyfert galaxies and
type-II QSOs. The QSOs have higher nuclear temperature and lower electron
density than Seyferts, but show no significant difference compared to type-II
QSOs, while the ionization parameter decreases with radial distance, similar to
the case of Seyfert galaxies. For PG1012+008, we determine the stellar velocity
dispersion of the host galaxy. Combined with the black hole mass, we find that
the luminous radio-quiet QSO follows the local M_BH-sigma* relation of active
galactic nuclei.
