We apply the observed optical/X-ray spectral states of the Galactic black h
ole candidates (GBHCs) to the cosmological QSO luminosity evolution under t
he assumptions that QSOs and GBHCs are powered by similar accretion process
es and that their emission mechanisms are also similar. The QSO luminosity
function (LF) evolution in various energy bands is strongly affected by the
spectral evolution, which is tightly correlated with the luminosity evolut
ion. We generate a random sample of QSOs born nearly synchronously by allow
ing the QSOs to have redshifts in a narrow range around an initial high red
shift, black hole masses according to a power law, and mass accretion rates
near Eddington rates. The QSOs evolve as a single long-lived population on
the cosmological timescale. The pure luminosity evolution results in disti
nct luminosity evolution features caused by the strong spectral evolution.
Most notably, different energy bands (optical/UV, soft X-ray, and hard X-ra
y) show different evolutionary trends, and the hard X-ray LF in particular
shows an apparent reversal of the luminosity evolution (from decreasing to
increasing luminosity) at low redshifts, which is not seen in the conventio
nal pure luminosity evolution scenario without spectral evolution. The resu
lting mass function of black holes (BHs), which is qualitatively consistent
with the observed QSO LF evolution, shows that QSO remnants are likely to
be found as BHs with masses in the range 10(8)-5 x 10(10) M.. The long-live
d single population of QSOs are expected to leave their remnants as superma
ssive BHs residing in rare, giant elliptical galaxies.