Second-order spin-wave expansions are used to compute the ground-state
energy and sublattice magnetizations of the quantum one-dimensional H
eisenberg ferrimagnet with nearest-neighbor antiferromagnetic interact
ions and two types of alternating sublattice spins S-1>S-2. It is foun
d that in the extreme quantum cases (S-1,S-2)=(1,1/2), (3/2,1), and (3
/2,1/2), the estimates for the ground-state energy and sublattice magn
etizations differ less than 0.03% for the energy and 0.2% for the subl
attice magnetizations from the recently published density-matrix renor
malization-group numerical calculations. The reported results strongly
suggest that the quantum Heisenberg ferrimagnetic chains give another
example of a low-dimensional quantum spin system where the spin-wave
approach demonstrates a surprising efficiency.