$\kappa$-Deformed quantum and classical mechanics for a system with position-dependent effective mass
Quantum Physics
2020-07-23 v1 Mathematical Physics
math.MP
Classical Physics
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 -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.
Cite
@article{arxiv.2007.11184,
title = {$\kappa$-Deformed quantum and classical mechanics for a system with position-dependent effective mass},
author = {Bruno G. da Costa and Ignacio S. Gomez and Mariela Portesi},
journal= {arXiv preprint arXiv:2007.11184},
year = {2020}
}