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