  We report on numerical studies of the energy spectrum and the localization
properties in the double-layer quantum Hall system at $\nu = 1$. The Coulomb
interaction is treated by the Hartree-Fock approximation, and the localization
properties in the presence of disorder are studied by evaluating participation
ratios for the Hartree-Fock eigenfunctions. We show that the extended states
seem to exist only near each center of the two subbands split by the
exchange-enhanced energy gap. It is also shown that the self-consistent
orbitals whose energies are close to the Fermi energy appear to become extended
together with the reduction in the energy gap as the layer separation
increases. The collapse of the energy gap expected from our results is
consistent with the incompressible-compressible transition observed in recent
experiments, and the change of the localization properties near the Fermi
energy can explain the disappearance of the quantum Hall effect for large layer
separations very well.
