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 \Phi ( L _ { B } ) \propto [ ( L _ { B } / L _ { B } ^ { * } ) ^ { \alpha } + ( L _ { B } / L _ { B } % ^ { * } ) ^ { \beta } ] ^ { -1 } .
Exponential luminosity evolution models , both as a function of look-back time , L _ { B } ^ { * } ( z ) = L _ { B } ^ { * } ( 0 ) { e } ^ { k _ { 1 } \tau } , and as a general second-order polynomial , L _ { B } ^ { * } ( z ) \propto 10 ^ { k _ { 1 } z + k _ { 2 } z ^ { 2 } } , 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 .