  We apply the observed optical/X-ray spectral states of the Galactic black
hole candidates (GBHCs) to the cosmological QSO luminosity evolution under the
assumptions that QSOs and GBHCs are powered by similar accretion processes 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 evolution. We
generate a random sample of QSOs born nearly synchronously by allowing the QSOs
to have redshifts in a narrow range around an initial high redshift, 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 time
scale. The pure luminosity evolution results in distinct luminosity evolution
features due to the strong spectral evolution. Most notably, different energy
bands (optical/UV, soft X-ray, and hard X-ray) 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 conventional pure luminosity evolution
scenario without spectral evolution. The resulting 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**8-5x10**10 solar masses. The long-lived single population of QSOs are
expected to leave their remnants as supermassive BHs residing in rare, giant
elliptical galaxies.
