  Strong evidence is presented for the localization of low energy quasiparticle
states in disordered $d$-wave superconductors. Within the framework of the
Bogoliubov-de Gennes (BdG) theory applied to the extended Hubbard model with a
finite concentration of non-magnetic impurities, we carry out a fully
self-consistent numerical diagonalization of the BdG equations on finite
clusters containing up to $50\times 50$ sites. Localized states are identified
by probing their sensitivity to the boundary conditions and by analyzing the
finite size dependence of inverse participation ratios.
