  The double exchange (DE) model with quantum local spins S is studied; an
equation of motion approach is used and decoupling approximations analogous to
Hubbard's are made. Our approximate one-electron Green function G is exact in
the atomic limit of zero bandwidth for all S and band filling n, and as n->0
reduces to a dynamical coherent potential approximation (CPA) due to Kubo; we
regard our approximation as a many-body generalisation 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 magnetization. The electronic structure is
investigated and four bands per spin are obtained centred on the atomic limit
peaks of the spectral function. A resistivity formula appropriate to the model
is derived from the Kubo formula and the paramagnetic state resistivity rho is
calculated; insulating states are correctly obtained at n=0 and n=1 for strong
Hund coupling. Our prediction for rho is much too small to be consistent with
experiments on manganites 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 his use of an unphysical density of states.
