  A self-consistent theory of the frequency dependent diffusion coefficient for
the Anderson localization problem is presented within the tight-binding model
of non-interacting electrons on a lattice with randomly distributed on-site
energy levels. The theory uses a diagrammatic expansion in terms of (extended)
Bloch states and is found to be equivalent to the expansion in terms of
(localized) Wannier states which was derived earlier by Kroha, Kopp and
W\"olfle. No adjustable parameters enter the theory. The localization length is
calculated in 1, 2 and 3 dimensions as well as the frequency dependent
conductivity and the phase diagram of localization in 3 dimensions for various
types of disorder distributions. The validity of a universal scaling function
of the length dependent conductance derived from this theory is discussed in
the strong coupling region. Quantitative agreement with results from numerical
diagonalization of finite systems demonstrates that the self-consistent
treatment of cooperon contributions is sufficient to explain the phase diagram
of localization and suggests that the system may be well described by a
one-parameter scaling theory in certain regions of the phase diagram, if one is
not too close to the transition point.
