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理论物理通讯：英文版

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

Jü, Guoxing, Xiang, Yang, Ren Ren, Zhong-Zhou

Published Jan 1, 2006• 5 citations
OpenAlex

Abstract

为一个没有伪的粒子的 s 波浪的性质 withposition 依赖的质量(PDM ) 在细节被讨论了。与为在起源附近的免费的量粒子的 s 波浪的本地化仅仅在发生在二种尺寸的经常的质量不同于系统，除了 D = ，有 PDM 的没有伪的粒子能在 Ddimensions 经历吸引人的力量 1 当它的集体功能满足一些条件时。与它的位置变化的一个粒子的有效的团能导致有效相互作用，它可能在一些情况中是吸引人的。为有特殊 PDM 的二维、三维的系统的 s 波浪的特徵函数和相应概率密度的分析表达式被给，并且在为这些系统的起源附近的本地化的存在被显示出。

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

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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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We recycle Cruz et al.'s (Phys. Lett. A 369 (2007) 400) work on the classical and quantum position-dependent mass (PDM) oscillators. To elaborate on the ordering ambiguity, we properly amend some of the results reported in their work and discuss the classical and quantum mechanical correspondence for the PDM harmonic oscillators. We use a point canonical transformation and show that one unique quantum PDM oscillator Hamiltonian (consequently, one unique ordering-ambiguity parametric set j=l=-1/4 and k=-1/2) is obtained. To show that such a parametric set is not just a manifestation of the quantum PDM oscillator Hamiltonian, we consider the classical and quantum mechanical correspondence for quasi-free PDM particles moving under the influence of their own PDM force fields.

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理论物理通讯：英文版•Jan 1, 2007•0 citations
为一个没有伪的粒子的 s 波浪的性质 withposition 依赖的质量(PDM ) 在细节被讨论了。与为在起源附近的免费的量粒子的 s 波浪的本地化仅仅在发生在二种尺寸的经常的质量不同于系统，除了 D = ，有 PDM 的没有伪的粒子能在 Ddimensions 经历吸引人的力量 1 当它的集体功能满足一些条件时。与它的位置变化的一个粒子的有效的团能导致有效相互作用，它可能在一些情况中是吸引人的。为有特殊 PDM 的二维、三维的系统的 s 波浪的特徵函数和相应概率密度的分析表达式被给，并且在为这些系统的起源附近的本地化的存在被显示出。
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.
We recycle Cruz et al.'s (Phys. Lett. A 369 (2007) 400) work on the classical and quantum position-dependent mass (PDM) oscillators. To elaborate on the ordering ambiguity, we properly amend some of the results reported in their work and discuss the classical and quantum mechanical correspondence for the PDM harmonic oscillators. We use a point canonical transformation and show that one unique quantum PDM oscillator Hamiltonian (consequently, one unique ordering-ambiguity parametric set j=l=-1/4 and k=-1/2) is obtained. To show that such a parametric set is not just a manifestation of the quantum PDM oscillator Hamiltonian, we consider the classical and quantum mechanical correspondence for quasi-free PDM particles moving under the influence of their own PDM force fields.