论文标题
$κ$ - 指定的量子和具有依赖位置有效质量的系统的经典力学
$κ$-Deformed quantum and classical mechanics for a system with position-dependent effective mass
论文作者
论文摘要
我们介绍了由Kappa统计数据激发的变形代数结构（称为$κ$ -Algebra）的粒子的量子和经典力学形式主义。从该结构中，我们获得了位置和动量运算符的变形版本，该版本允许定义一个指数的规范变换，该转换将变形空间中恒定质量的粒子映射到标准空间中具有位置依赖性质量的粒子。我们用限制在无限势孔中的粒子来说明形式主义，而马修斯 - 拉克曼南振荡器表现出不确定性关系，具体取决于变形。
We present the quantum and classical mechanics formalisms for a particle with position-dependent mass in the context of a deformed algebraic structure (named $κ$-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.
