  We apply a recently developed approach (Liaw 2013) to study the existence of
extended states for the three dimensional discrete random Schroedinger operator
at small disorder. The conclusion of delocalization at small disorder agrees
with other numerical and experimental observations. Further the work furnishes
a verification of the numerical approach and its implementation.
  Not being based on scaling theory, this method eliminates problems due to
boundary conditions, common to previous numerical methods in the field. At the
same time, as with any numerical experiment, one cannot exclude finite-size
effects with complete certainty. Our work can be thought of as a new and quite
different use of Lanczos' algorithm; a posteriori tests to show that the
orthogonality loss is very small.
  We numerically track the "bulk distribution" (here: the distribution of where
we most likely find an electron) of a wave packet initially located at the
origin, after iterative application of the discrete random Schroedinger
operator.
