Droplet wave functions for the fractional quantum Hall effect

Trial wave functions which, in the thermodynamic limit, describe states relevant to the fractional quantum Hall effect are explicitly constructed for up to eight electrons. Estimates are given for the ground-state energies and pair-correlation functions and for the low-lying excitation energies for states associated with the filling factors {ν}=(1/3), (2/7), and (2/5). The results help explain why the filling factors {ν}=νₘ=m/(2m+1), m=1,2,..., and {ν}=1-νₘ show strong quantum Hall effects.