  We present a determination of the optical QSO luminosity function and its
cosmological evolution with redshift for a sample of over 6000 QSOs identified
primarily from the first observations of the 2dF QSO Redshift Survey (2QZ). For
QSOs with -26 < M_B < -23 and 0.35 < z < 2.3, we find that pure luminosity
evolution (PLE) models provide an acceptable fit to the observed redshift
dependence of the luminosity function. The luminosity function is best fit by a
two-power-law function of the form. Exponential luminosity evolution models,
both as a function of look-back time, and as a general second-order polynomial
with redshift, were found to provide acceptable fits to the dataset comprising
the 2QZ and the Large Bright Quasar Survey. Exponential evolution with
look-back time is prefered for q_0=0.05, while the polynomial evolution model
is prefered for q_0=0.5. The shape and evolution of the LF at low redshifts
(z<0.5) and/or high luminosities, not currently well sampled by the 2dF QSO
survey, may show departures from pure luminosity evolution, but the results
presented here show that over a significant range of redshift, PLE is a good
description of QSO evolution.
