  The calculations of the local and global properties of two band
superconductors have been presented with particular attention to the role of
the inter-orbital scattering of pairs. The properties of such superconductors
are very different from a single band or typical two band systems with dominant
intra-band pairing interactions. The role of Van Hove singularity in one of the
bands on the properties of intra-band clean superconductor has been discussed.
It leads to marked increase of superconducting transition temperature in the
weak coupling limit. We study the inhomogeneous systems in which the
characteristics change from place to place by solving the Bogolubov-de Gennes
equations for small clusters. The suppression of the superconducting order
parameter by the single impurity scattering the fermions between bands is
contrasted with that due to intra-band impurity scattering. The results
obtained for impure systems have been shown as a maps of local density of
states, the order parameter and gap function. They can be directly compared
with STM spectra of the real material.
