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arXiv · 2007.11184

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

Bruno G. da Costa·Ignacio S. Gomez·Mariela Portesi
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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.

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Bruno G. da Costa, Ignacio S. Gomez, Mariela Portesi. 2020-07-22. $\kappa$-Deformed quantum and classical mechanics for a system with position-dependent effective mass. https://doi.org/10.1063/5.0014553

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