  We investigate the accuracy of the coherent potential approximation (CPA) for
a one-dimensional array with nearest-neighbor interactions and a Gaussian
distribution of fluctuations in the on-site potential. The CPA values of the
integrated density of states and the inverse localization length are compared
with the results of mode-counting studies carried out on arrays of 107 - 108
sites. Good agreement is obtained suggesting that the CPA may be exact for this
model. We also consider the asymptotic behavior of the inverse localization
length and show that it can be approximated by the reciprocal of the decay
length of a state localized about a single, strongly perturbed site in an
otherwise perfect lattice.
