  The nature of the fractional quantum Hall effect at $\nu=1/2$ observed in
wide quantum wells almost three decades ago is still under debate. Previous
studies have investigated it by the variational Monte Carlo method, which makes
the assumption that the transverse wave function and the gap between the
symmetric and antisymmetric subbands obtained in a local density approximation
at zero magnetic field remain valid even at high perpendicular magnetic fields;
this method also ignores the effect of Landau level mixing. We develop in this
work a three-dimensional fixed phase Monte Carlo method, which gives, in a
single framework, the total energies of various candidate states in a finite
width quantum well, including Landau level mixing, directly in a large magnetic
field. This method can be applied to one-component states, as well
two-component states in the limit where the symmetric and antisymmetric bands
are nearly degenerate. Our three-dimensional fixed-phase diffusion Monte Carlo
calculations suggest that the observed 1/2 fractional quantum Hall state in
wide quantum wells is likely to be the one-component Pfaffian state supporting
non-Abelian excitations. We hope that this will motivate further experimental
studies of this state.
