  We perform an exact spherical geometry finite-size diagonalization
calculation for the fractional quantum Hall ground state in three different
experimentally relevant GaAs-Al_{x}Ga_{1-x}As systems: a wide parabolic quantum
well, a narrow square quantum well, and a heterostructure. For each system we
obtain the Coulomb pseudopotential parameters entering the exact
diagonalization calculation by using the realistic subband wave function from a
self-consistent electronic structure calculation within the local density
approximation (LDA) for a range of electron densities. We compare our realistic
LDA pseudopotential parameters with those from widely used simpler model
approximations in order to estimate the accuracies of the latter. We also
calculate the overlap between the exact numerical ground state and the
analytical Laughlin state as well as the excitation gap as a function of
density. For the three physical systems we consider the calculated overlap is
found to be large in the experimental electron density range. We compare our
calculated excitation gap energy to the experimentally obtained activated
transport energy gaps after subtracting out the effect of level broadening due
to collisions. The agreement between our calculated excitation gaps and the
experimental measurements is excellent.
