Non-additive quantum mechanics for a position-dependent mass system: Dirac delta and quasi-periodic potentials

2020 ◽  
Vol 129 (1) ◽  
pp. 10003 ◽  
Author(s):  
Bruno G. da Costa ◽  
Ignacio S. Gomez ◽  
Maike A. F. dos Santos
Keyword(s):  
Quantum Mechanics ◽  
Mass System ◽  
Dirac Delta ◽  
Periodic Potentials ◽  
Dependent Mass ◽  
Position Dependent Mass

Path integral for quantum dynamics with position-dependent mass within the displacement operator approach

2020 ◽  
Vol 35 (30) ◽  
pp. 2050246
Author(s):  
H. Benzair ◽  
M. Merad ◽  
T. Boudjedaa
Keyword(s):  
Quantum Mechanics ◽  
Path Integral ◽  
Quantum Dynamics ◽  
Translation Operator ◽  
Integral Approach ◽  
Operator Approach ◽  
Square Well ◽  
Dependent Mass ◽  
Position Dependent Mass ◽  
Coulomb Potentials

In the context of quantum mechanics reformulated in a modified Hilbert space, we can formulate the Feynman’s path integral approach for the quantum systems with position-dependent mass particle using the formulation of position-dependent infinitesimal translation operator. Which is similar a deformed quantum mechanics based on modified commutation relations. An illustration of calculation is given in the case of the harmonic oscillator, the infinite square well and the inverse square plus Coulomb potentials.

scholarly journals Effects of the Cornell-Type Potential on a Position-Dependent Mass System in Kaluza-Klein Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
E.V. B. Leite ◽  
H. Belich ◽  
R. L. L. Vitória
Keyword(s):  
Magnetic Field ◽  
Quantum Effect ◽  
Scalar Particle ◽  
Relativistic Energy ◽  
Mass System ◽  
Klein Theory ◽  
Dependent Mass ◽  
Type Potential ◽  
Position Dependent Mass ◽  
Kaluza Klein

In this paper, we have investigated a scalar particle with position-dependent mass subject to a uniform magnetic field and a quantum flux, both coming from the background which is governed by the Kaluza-Klein theory. By modifying the mass term of the scalar particle, we insert the Cornell-type potential. In the search for solutions of bound states, we determine the relativistic energy profile of the system in this background of extra dimension. Particular cases of this system are analyzed and a quantum effect can be observed: the dependence of the magnetic field on the quantum numbers of the solutions.

scholarly journals A squeeze-like operator approach to position-dependent mass in quantum mechanics

2014 ◽  
Vol 55 (8) ◽  
pp. 082103 ◽  
Author(s):  
Héctor M. Moya-Cessa ◽  
Francisco Soto-Eguibar ◽  
Demetrios N. Christodoulides
Keyword(s):  
Quantum Mechanics ◽  
Operator Approach ◽  
Dependent Mass ◽  
Position Dependent Mass

scholarly journals Quantum solvability of a general ordered position dependent mass system: Mathews-Lakshmanan oscillator

2017 ◽  
Vol 58 (10) ◽  
pp. 102110 ◽  
Author(s):  
S. Karthiga ◽  
V. Chithiika Ruby ◽  
M. Senthilvelan ◽  
M. Lakshmanan
Keyword(s):  
Mass System ◽  
Dependent Mass ◽  
Position Dependent Mass
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