We present the quantum and classical mechanics formalisms for a particle with position-dependent mass in the context of a deformed algebraic structure (named $\kappa$-algebra), motivated by the Kappa-statistics. From this structure we obtain deformed versions of the position and momentum operators, which allow to define a point canonical transformation that maps a particle with constant mass in a deformed space into a particle with position-dependent mass in the standard space. We illustrate the formalism with a particle confined in an infinite potential well and the Mathews-Lakshmanan oscillator, exhibiting uncertainty relations depending on the deformation.

中文翻译：

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具有位置相关有效质量的系统的κ-变形量子力学和经典力学

我们在变形代数结构（命名为 $\kappa$-algebra）的背景下，由 Kappa-statistics 提出了具有位置相关质量的粒子的量子和经典力学形式。从这个结构中，我们获得了位置和动量算子的变形版本，它允许定义一个点规范变换，将变形空间中具有恒定质量的粒子映射到标准空间中具有位置相关质量的粒子。我们用限制在无限势阱中的粒子和 Mathews-Lakshmanan 振荡器来说明形式主义，表现出取决于变形的不确定性关系。