Bohmian formalism and Fisher information from q-deformed Schrodinger equation

被引：8

作者：

da Costa, Bruno G. ^{[1
]}

Gomez, Ignacio S. ^{[2
,3
]}

机构：

[1] Inst Fed Educ Ciencia & Tecnol Sertao Pernambucan, BR 407,Km 08, BR-56314520 Petrolina, PE, Brazil

[2] Univ Fed Bahia, Inst Fis, Rua Barao Jeremoabo, BR-40170175 Salvador, BA, Brazil

[3] Natl Inst Sci & Technol Complex Syst, Sao Paulo, Brazil

来源：

PHYSICS LETTERS A | 2018年 / 382卷 / 37期

关键词：

q-Deformed Schrodinger equation; Bohmian mechanics; Fisher information; Cramer-Rao bound; POSITION-DEPENDENT MASS; QUANTUM-THEORY; MECHANICS; ALGEBRA;

D O I：

10.1016/j.physleta.2018.07.031

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We discuss the Bohmian mechanics using a deformed Schrodinger equation for position-dependent mass systems, in the context of a q-algebra inspired by the nonextensive statistical mechanics. We obtain the Bohmian quantum formalism by means of a deformed version of the Fisher information functional, from which a deformed Cramer-Rao bound is derived. Lagrangian and Hamiltonian formulations, inherited by the q-algebra, are also developed. Then, we illustrate the results with a particle confined in an infinite square potential well. The preservation of the deformed Cramer-Rao bound for eigenstates shows the role played by the q-algebraic structure. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：2605 / 2612

页数：8

共 41 条

[1] Solution of the Dirac equation with position-dependent mass in the Coulomb field [J].

Alhaidari, AD .

PHYSICS LETTERS A, 2004, 322 (1-2) :72-77

[2] Investigation of Bohr-Mottelson Hamiltonian in γ-rigid version with position dependent mass [J].

Alimohammadi, M. ;

Hassanabadi, H. ;

Zare, S. .

NUCLEAR PHYSICS A, 2017, 960 :78-89

[3] The inversion potential for NH3 using a DFT approach [J].

Aquino, N ;

Campoy, G ;

Yee-Madeira, H .

CHEMICAL PHYSICS LETTERS, 1998, 296 (1-2) :111-116

[4] Structure and energetics of mixed He-4-He-3 drops [J].

Barranco, M ;

Pi, M ;

Gatica, SM ;

Hernandez, ES ;

Navarro, J .

PHYSICAL REVIEW B, 1997, 56 (14) :8997-9003

[5] The extended Thomas-Fermi kinetic energy density functional with position-dependent effective mass in one dimension [J].

Bencheikh, K ;

Berkane, K ;

Bouizane, S .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2004, 37 (45) :10719-10725

[6] SPACE-CHARGE EFFECTS ON ELECTRON TUNNELING [J].

BENDANIEL, DJ ;

DUKE, CB .

PHYSICAL REVIEW, 1966, 152 (02) :683-+

[7]

BOHM D, 1952, PHYS REV, V85, P166, DOI 10.1103/PhysRev.85.166

[8] A possible deformed algebra and calculus inspired in nonextensive thermostatistics [J].

Borges, EP .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2004, 340 (1-3) :95-101

[9] Position-dependent mass, finite-gap systems, and supersymmetry [J].

Bravo, Rafael ;

Plyushchay, Mikhail S. .

PHYSICAL REVIEW D, 2016, 93 (10)

[10]

Costa Filho R. N., 2011, PHYS REV A, V84

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