  We present an extensive numerical study of the ferromagnetic Kondo lattice
model with quantum mechanical S=3/2 core spins. We treat one orbital per site
in one dimension using the density matrix renormalization group and include
on-site Coulomb repulsion between the electrons. We examine parameters relevant
to manganites, treating the range of low to intermediate doping, 0<x<0.5. In
particular, we investigate whether quantum fluctuations favor phase separation
over the ferromagnetic polarons observed in a model with classical core spins.
We obtain very good agreement of the quantum model with previous results for
the classical model, finding separated polarons which are repulsive at short
distance for finite t_2g superexchange J'. Taking on-site Coulomb repulsion
into account, we observe phase separation for small but finite superexchange
J', while for larger J' polarons are favored in accordance with simple energy
considerations previously applied to classical spins. We discuss the
interpretation of compressibilities and present a phase diagram with respect to
doping and the t_2g superexchange parameter J' with and without Coulomb
repulsion.
