  We present a small polaron picture and show that finite bandwidth effects are
important to understand colossal magnetoresistance. Besides the polaron size
parameter, we show that there is another parameter (adiabaticity parameter)
that is relevant to studying magnetoresistance. We find that for fixed values
of the polaron size parameter an increase in the adiabaticity parameter
increases the magnetoresistance. The magnetic transition is studied within a
mean field approach. We point out important oversights in the literature. We
find that for the reported values of the bandwidth (based on band structure
calculations) and for experimentally determined values of activation energy and
Debye frequency, the calculated values of the magnetoresistance compare
favorably with experimental ones. We calculate the optical conductivity too and
find that there is reasonable agreement with experiment.
