Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Localization of $s$-Wave and Quantum Effective Potential of a
  Quasi-Free Particle with Position-Dependent Mass   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.

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The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
2
The categories of this paper are: math
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The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg