A quantum form of the Hamiltonian for a double-exchange ͑DE͒ system, based on the results of Anderson and Hasegawa's semiclassical treatment, is presented together with several predictions. The magnetization decreases mainly in 3/2 and 5/2 powers of temperature at low temperature but includes a T 3 term. The Curie temperature, in a rescaled DE coupling energy (ͱ2b/2S 2 )J d unit, is dependent on hole concentration x and has highest value that is about 1/3 that of ordinary Heisenberg magnet at xϭ0.5. The susceptibility at high temperatures lacks a 1/T 2 term and has a characteristic temperature in rescaled DE coupling units that is about 3/4 that of Heisenberg magnet in molecular-field theory.