  The question about the existence of Bogoliubov's quasiparticles in the BCS
wave functions underneath Gutzwiller's projection is of importance to strongly
correlated systems. We develop a method to examine the two-particle excitations
of Gutzwiller-projected BCS wave functions by using the variational Monte Carlo
approach. We find that the exact Gutzwiller-projected quasiparticle (GQP)
dispersions are quantitatively reproduced by the Gutzwiller-projected
Bogoliubov quasiparticles (GBQP) except the regions where d-wave Cooper pairing
is strong. Since GQP still shows higher energy than GBQP near the antinodes, we
believe GBQP provides a reasonable description to the low-energy excitations in
strongly correlated superconducting systems. In addition, the intimate
connection between Gutzwiller's projection and d-wave Cooper pairing may also
imply that strong correlations play a significant role in the nodal-antinodal
dichotomy seen by photoemission experiments in cuprates.
