  The properties of the s-wave for a quasi-free particle with
position-dependent mass(PDM) have been discussed in details. Differed from the
system with constant mass in which the localization of the s-wave for the free
quantum particle around the origin only occurs in two dimensions, the
quasi-free particle with PDM can experience attractive forces in $D$ dimensions
except D=1 when its mass function satisfies some conditions. The effective mass
of a particle varying with its position can induce effective interaction which
may be attractive in some cases. The analytical expressions of the
eigenfunctions and the corresponding probability densities for the s-waves of
the two- and three-dimensional systems with a special PDM are given, and the
existences of localization around the origin for these systems are shown.
