  We revisit the Anderson-Hasegawa double-exchange model and critically examine
its exact solution when the core spins are treated quantum mechanically.We show
that the quantum effects, in the presence of an additional superexchange
interaction between the core spins, yield a term, the significance of which has
been hitherto ignored. The quantum considerations further lead to new results
when polaronic effects, believed to be ubiquitous in manganites due to
electron-phonon coupling, are included. The consequence of these results for
the magnetic phase diagrams and the thermal heat capacity is also carefully
analysed.
