The problem of propagation for quasiparticles on a dimerized chain whi
ch is modeled by alternating site energies and intersite interactions
is investigated. Exact solutions for the propagators, the mean polariz
ation and mean-square displacement are obtained, from which the role o
f the site-energy mismatch and hopping disturbance on the behavior of
the moving particle can be clearly seen. It is demonstrated that the i
ncrease of the site-energy mismatch and the hopping disturbance will l
ead to the enhancement of the localization.