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The Localization of $s$-Wave and Quantum Effective Potential of a Quasi-Free Particle with Position-Dependent Mass

Guo-Xing JU·Yang Xiang·Zhong-Zhou Ren
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Abstract

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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Guo-Xing JU, Yang Xiang, Zhong-Zhou Ren. 2005-12-31. The Localization of $s$-Wave and Quantum Effective Potential of a Quasi-Free Particle with Position-Dependent Mass. https://doi.org/10.1088/0253-6102%2F46%2F5%2F010

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