The double exchange (DE) model with quantum local spins S is studied; an eq
uation of motion approach is used and decoupling approximations analogous t
o Hubbard's are made. Our approximate one-electron Green function G is exac
t in the atomic limit of zero bandwidth for all 5 and band filling n. Since
as n --> 0 it reduces to the result of a dynamical coherent potential appr
oximation (CPA) due to Kubo, we regard our approximation as a many-body gen
eralization of Kubo's CPA. G is calculated self-consistently for general S
in the paramagnetic state and for S = 1/2 in a state of arbitrary magnetiza
tion. The electronic structure is investigated and four bands per spin are
obtained centred on the atomic limit peaks of the spectral function. A resi
stivity formula appropriate to the model is derived from the Kubo formula a
nd the paramagnetic state resistivity rho is calculated; insulating states
are correctly obtained at n = 0 and n = 1 for strong Hund coupling. Our pre
diction for rho is much too small to be consistent with experiments on mang
anites so we agree with Millis et al that the bare DE model is inadequate.
We show that the agreement with experiment obtained by Furukawa is due to h
is use of an unphysical density of stares.