Localization of s-Wave and Quantum Effective Potential of a Quasi-free Particle with Position-Dependent Mass |
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Authors: | JU Guo-Xing XIANG Yang REN Zhong-Zhou |
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Institution: | Department of Physics,Nanjing University,Nanjing,210093,China Department of Physics,Nanjing University,Nanjing,210093,China Department of Physics,Nanjing University,Nanjing,210093,China |
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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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Keywords: | position-dependent mass s-wave Schrodinger equation dimensionality of the space localization eigenfunction probability density |
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