Mapping between charge-monopole and position-dependent mass systems

Schmidt, Alexandre G. M.; Jesus, Anderson L. de

doi:10.1063/1.5039622

Cited by 21 publications

(10 citation statements)

References 33 publications

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“…2 Further studies in noncommuting quantum spaces led to a Schrödinger equation with a position-dependent effective mass (PDM). 3 Along the last decades, the PDM systems have attracted attention because of their wide range of applicability in semiconductor theory, [4][5][6][7] nonlinear optics, 8 quantum liquids, 9,10 inversion potential for NH 3 in density functional theory, 11 particle physics, 12 many body theory, 13 molecular physics, 14 Wigner functions, 15 relativistic quantum mechanics, 16 superintegrable systems, 17 nuclear physics, 18 magnetic monopoles, 19,20 astrophysics, 21 nonlinear oscillations, [22][23][24][25][26][27][28][29][30][31] factorization methods and supersymmetry, [32][33][34][35][36] coherent states, [37][38][39] etc.…”

Section: Introductionmentioning

confidence: 99%

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

Costa

Gomez

Portesi

2020

Journal of Mathematical Physics

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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.

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Section: Introductionmentioning

confidence: 99%

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

Costa

Gomez

Portesi

2020

Journal of Mathematical Physics

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“…Autores/ano Carga-monopolo Schmidt, Jesus/2018 [48] Carga-dyon Jesus, Schmidt/2019 [49] Carga-monopolo relativístico Jesus, Schmidt/2019 [49] Carga-monopolo com spin-1/2 Jesus, Schmidt/2019 [50] informações a respeito de seu comportamento, inúmeros modelos análogos teóricos e experimentais (tanto clássicos como quânticos) podem ser obtidos.…”

Section: Sistema Alvounclassified

Introdução à Física do Monopolo Magnético: uma abordagem clássica

Jesus

Schmidt

Portugal

2023

Rev. Bras. Ensino Fís.

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Neste trabalho apresentaremos uma introdução à Física do Monopolo Magnético no regime não – relativístico. O tratamento clássico de um sistema composto por uma partícula pontual eletricamente carregada na presence de um monopolo magnético na origem, com suas equações de movimento e o estudo do potencial vetor de Dirac, será desenvolvido ao longo do presente trabalho. A questão das singularidades e as transformações de calibre serão também tratadas. Ao final, listaremos alguns modelos análogos ao monopolo magnético, utilizando outros sistemas físicos.

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“…Position-dependent mass (PDM) models have been under regular development since the sixties and continuously improved up to present days. Particularly, in the last decade modeling quantum systems with PDM particles has grown as a consequence of its wide area of applications [11][12][13][14][15][16]. Among them, this technique has been applied to the understanding of the electronic properties of semiconductor heterostructures, crystal-growth techniques [5,17], quantum wells and quantum dots [18][19][20][21][22][23][24][25][26][27][28], helium clusters [29], graded crystals [30], quantum liquids [31], nanowire structures with size variations, impurities, dislocations, and geometry imperfections [32][33][34][35], as well as in superconductors investigations [4,5,7,17,30,[36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

The kinetic Hamiltonian with position-dependent mass

Lima,

Christiansen

2023

Preprint

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In the present paper we examine in a systematic way the most relevant orderings of pure kinetic Hamiltonians for five different position-dependent mass (PDM) profiles: soliton-like, reciprocal quadratic and biquadratic, exponential and parabolic. As a result of the non-commutativity between momentum and position operators, a diversity of effective potentials is generated. We analyse the whole set and find unexpected coincidences as well as discrepancies among them. We obtain analytically the full-spectrum of energies and solutions in the twenty-five cases considered.It is shown how the simple ordinary constant-mass solutions are transformed into a variety of complex combinations of transcendental functions and arguments. We find that particles with a non-uniform mass density can present discrete energy spectra as well as continuous ones which can be bounded or not. These results are consistent with the fact that although the external potential is zero, PDM eigenfunctions are not actual free states but a sort of effective waves in a solid-state sample. This is precisely the origin of the position-dependent mass. In all the events we obtain exact complete spectral expressions. Our methodological procedure thus puts a wide diversity of Hamiltonian seeds on an equal footing in order to be compared. This allows choosing the better arrangement to model a specific solid or heterostructure once the spectrum of a given material is experimentally available. Finally, we perform a one-dimensional model calculation of a double heterostructure with a parabolic PDM particle in the interface region. Our study is also indicated for applications inside material structures with the addition of external potentials.

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Mapping between charge-monopole and position-dependent mass systems

Cited by 21 publications

References 33 publications

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

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

Introdução à Física do Monopolo Magnético: uma abordagem clássica

The kinetic Hamiltonian with position-dependent mass

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