κ-Deformed quantum and classical mechanics for a system with position-dependent effective mass

Abstract

We present the quantum and classical mechanics formalisms for a particle with a 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 us to define a point canonical transformation that maps a particle with a constant mass in a deformed space into a particle with a 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.

Investigation of the Infinite Discrete Levels from Finite Discrete Levels in Position Dependent Mass Quantum Systems

“…In this paper we have shown that DDL quantum systems can reflect infinite distinct discrete energy levels under suitable form of position dependent mass. The model mass [15] and used by others [1,3,7,9]. It is worth mentioning that only this typical form of T can be derived [8].…”

“…It should be borne in mind that all the figures on PDM actually we have plotted with T i.e p 2 M = T . In order to convince the reader about our method [1,3], we consider two simple models as…”

“…In fact, for N=1 model Hamiltonian was also previously proposed by Mathews and Lakshnman for the study of nonlinear analysis in view of its potential applications in quantum field theory [4]. As such the Hamiltonian is not self-adjoint(H P DM ̸ = H † P DM ) [1,3,7,9,[13][14][15]. In its self adjoint form, it is expressed as [15]:…”

Supersymmetric quantum mechanics and coherent states for a deformed oscillator with position-dependent effective mass

“…Furthermore, effects of the gravitational field in quantum mechanics have been characterized by generalizations of the standard commutation relationship between the position and the linear momentum, giving place to the generalized uncertainty principles (GUP). [46][47][48][49][50][51][52][53] In this context, some theoretical frameworks have been developed to mimic the effect of the PDM by means of deformed algebraic structures. [51][52][53] One of these formulations is derived from a a) Electronic mail: bruno.costa@ifsertao-pe.edu.br b) Electronic mail: cardoso.genilson@outlook.com c) Electronic mail: ignacio.sebastian@ufba.br translation operator that causes non-additive displacements of the type Tγ (ε)|x = |x + (1 + γx)ε , being γ a deformation parameter with inverse length dimension.…”

“…[46][47][48][49][50][51][52][53] In this context, some theoretical frameworks have been developed to mimic the effect of the PDM by means of deformed algebraic structures. [51][52][53] One of these formulations is derived from a a) Electronic mail: bruno.costa@ifsertao-pe.edu.br b) Electronic mail: cardoso.genilson@outlook.com c) Electronic mail: ignacio.sebastian@ufba.br translation operator that causes non-additive displacements of the type Tγ (ε)|x = |x + (1 + γx)ε , being γ a deformation parameter with inverse length dimension. [54][55][56][57][58][59][60][61][62][63][64][65][66][67] This translation operator leads to a position-dependent linear momentum operator pγ that generates non-additive translations.…”