$\kappa$-Deformed quantum and classical mechanics for a system with position-dependent effective mass

TL;DR

This paper develops quantum and classical mechanics frameworks for particles with position-dependent mass within a $$-deformed algebraic structure, illustrating the formalism with specific systems and deformation-dependent uncertainty relations.

Contribution

It introduces a novel formalism combining position-dependent mass with $$-deformed algebra, including operator definitions and transformations between deformed and standard spaces.

Findings

Deformed operators enable mapping between constant and position-dependent mass systems.

Uncertainty relations are affected by the deformation parameter.

Illustrations include infinite potential well and Mathews-Lakshmanan oscillator.

Abstract

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.