  The spatial variations of the order parameter, and the local density of
states (LDOS) on the corner of s-wave or $d_{x^2-y^2}$-wave superconductors, as
well as in superconductor-insulator-normal metal interfaces, are calculated
self consistently using the Bogoliubov-deGennes formalism within the two
dimensional extended Hubbard model. The exact diagonalization method is used.
Due to the suppression of the dominant d-wave order parameter, the extended
s-wave order parameter is induced near the surface, that alternates its sign
for the topmost sites at adjacent edges of the lattice and decays to zero in
the bulk. The presence of surface roughness results into the appearance of the
zero band conduction peak (ZBCP) near the corner surface which lacks from the
predictions of the quasiclassical theory.
