Relativistic oscillators in new type of the extended uncertainty principle

2019 ◽  
Vol 34 (32) ◽  
pp. 1950218 ◽  
Author(s):  
A. Merad ◽  
M. Aouachria ◽  
M. Merad ◽  
T. Birkandan
Keyword(s):  
Uncertainty Principle ◽  
Laguerre Polynomials ◽  
Operator Method ◽  
Wave Functions ◽  
Uniform Electric Field ◽  
Physical Parameters ◽  
Eigenvalues And Eigenfunctions ◽  
Klein Gordon ◽  
New Type ◽  
Extended Uncertainty

We present the exact solutions of one-dimensional Klein–Gordon and Dirac oscillators subject to the uniform electric field in the context of the new type of the extended uncertainty principle using the displacement operator method. The energy eigenvalues and eigenfunctions are determined for both cases. For the Klein–Gordon oscillator case, the wave functions are expressed in terms of the associated Laguerre polynomials and for the Dirac oscillator case, the wave functions are obtained in terms of the confluent Heun functions. The limiting cases are also studied using the special values of the physical parameters.

scholarly journals Effects of extended uncertainty principle on the relativistic Coulomb potential

2021 ◽  
Vol 36 (03) ◽  
pp. 2150018
Author(s):  
B. Hamil ◽  
M. Merad ◽  
T. Birkandan
Keyword(s):  
Uncertainty Principle ◽  
Coulomb Potential ◽  
State Energy ◽  
Bound State ◽  
Wave Functions ◽  
De Sitter ◽  
Dirac Equations ◽  
Klein Gordon ◽  
Relativistic Coulomb ◽  
Extended Uncertainty

The relativistic bound-state energy spectrum and the wave functions for the Coulomb potential are studied for de Sitter and anti-de Sitter spaces in the context of the extended uncertainty principle. Klein–Gordon and Dirac equations are solved analytically to obtain the results. The electron energies of hydrogen-like atoms are studied numerically.

Klein–Gordon field in spinning cosmic-string space-time with the Cornell potential

2018 ◽  
Vol 15 (10) ◽  
pp. 1850165 ◽  
Author(s):  
Mansoureh Hosseinpour ◽  
Hassan Hassanabadi ◽  
Marc de Montigny
Keyword(s):  
Scalar Field ◽  
Cosmic String ◽  
Quantum Dynamics ◽  
Topological Defects ◽  
Space Time ◽  
Wave Functions ◽  
Physical Parameters ◽  
Gravitational Fields ◽  
Cornell Potential ◽  
Klein Gordon

We study the relativistic quantum dynamics of a Klein–Gordon scalar field subject to a Cornell potential in spinning cosmic-string space-time, in order to better understand the effects of gravitational fields produced by topological defects on the scalar field. We solve the Klein–Gordon equation in the presence of scalar and vector interactions by utilizing the Nikiforov–Uvarov formalism and two ansätze, one of which leads to a biconfluent Heun differential equation. We obtain the wave-functions and the energy levels of the relativistic field in that space-time. We discuss the effect of various physical parameters and quantum numbers on the wave-functions.

Klein–Gordon oscillator in the presence of the minimal momentum

2019 ◽  
Vol 34 (25) ◽  
pp. 1950204 ◽  
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi ◽  
Nasrin Farahani
Keyword(s):  
Magnetic Field ◽  
Uncertainty Principle ◽  
Energy Levels ◽  
Two Dimensional ◽  
Higher Dimensional ◽  
Klein Gordon ◽  
Extended Uncertainty ◽  
The Magnetic Field

In this paper, we use the higher-dimensional extended uncertainty principle to discuss the two-dimensional Klein–Gordon oscillator in the absence of the magnetic field and in the presence of the magnetic field. We find the energy levels with the extended uncertainty principle correction for two cases.

Quantum Theory

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Principle ◽  
Quantum Spin ◽  
Quantum States ◽  
Wave Functions ◽  
Symbolic Representations ◽  
Quantum Numbers ◽  
The Subject ◽  
Heisenberg's Uncertainty Principle

The subject of Chapter 8 is the fundamental principles of quantum theory, the abstract extension of quantum mechanics. Two of the entities explored are kets and operators, with kets being representations of quantum states as well as a source of wave functions. The quantum box and quantum spin kets are specified, as are the quantum numbers that identify them. Operators are introduced and defined in part as the symbolic representations of observable quantities such as position, momentum and quantum spin. Eigenvalues and eigenkets are defined and discussed, with the former identified as the possible outcomes of a measurement. Bras, the counterpart to kets, are introduced as the means of forming probability amplitudes from kets. Products of operators are examined, as is their role underpinning Heisenberg’s Uncertainty Principle. A variety of symbol manipulations are presented. How measurements are believed to collapse linear superpositions to one term of the sum is explored.

scholarly journals A Dynamical Study of Fusion Hindrance with Nakajima-Zwanzig Projection Method

2021 ◽  
Author(s):  
Yasuhisa Abe ◽  
David Boilley ◽  
Quentin Hourdillé ◽  
Caiwan Shen
Keyword(s):  
Cross Sections ◽  
Degrees Of Freedom ◽  
Operator Method ◽  
Initial Distribution ◽  
Physical Parameters ◽  
Relaxation Processes ◽  
Fast Variable ◽  
Dynamical Study ◽  
Injection Point ◽  
Slow Variables

Abstract A new framework is proposed for the study of collisions between very heavy ions which lead to the synthesis of Super-Heavy Elements (SHE), to address the fusion hindrance phenomenon. The dynamics of the reaction is studied in terms of collective degrees of freedom undergoing relaxation processes with different time scales. The Nakajima-Zwanzig projection operator method is employed to eliminate fast variable and derive a dynamical equation for the reduced system with only slow variables. There, the time evolution operator is renormalised and an inhomogeneous term appears, which represents a propagation of the given initial distribution. The term results in a slip to the initial values of the slow variables. We expect that gives a dynamical origin of the so-called “injection point s” introduced by Swiatecki et al in order to reproduce absolute values of measured cross sections for SHE. A formula for the slip is given in terms of physical parameters of the system, which confirms the results recently obtained with a Langevin equation, and permits us to compare various incident channels.

Electromagnetic interaction with the Klein–Gordon equation in the framework of GUP

2021 ◽  
Vol 18 (12) ◽  
Author(s):  
B. Khosropour
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Uncertainty Principle ◽  
Electric Potential ◽  
Uniform Magnetic Field ◽  
Gordon Equation ◽  
Electromagnetic Interaction ◽  
Generalized Uncertainty Principle ◽  
Klein Gordon ◽  
Klein Gordon Equation

In this work, according to the generalized uncertainty principle, we study the Klein–Gordon equation interacting with the electromagnetic field. The generalized Klein–Gordon equation is obtained in the presence of a scalar electric potential and a uniform magnetic field. Furthermore, we find the relation of the generalized energy–momentum in the presence of a scalar electric potential and a uniform magnetic field separately.

scholarly journals l-state Solutions of the Relativistic and Non-Relativistic Wave Equations for Modified Hylleraas-Hulthen Potential Using the Nikiforov-Uvarov Quantum Formalism

2018 ◽  
Vol 3 (1) ◽  
pp. 03-09 ◽  
Author(s):  
Hitler Louis ◽  
Ita B. Iserom ◽  
Ozioma U. Akakuru ◽  
Nelson A. Nzeata-Ibe ◽  
Alexander I. Ikeuba ◽  
...  
Keyword(s):  
Wave Equations ◽  
Approximation Scheme ◽  
Jacobi Polynomials ◽  
Energy Eigenvalue ◽  
Relativistic Wave Equations ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
Relativistic Wave ◽  
Type Approximation ◽  
Klein Gordon

An exact analytical and approximate solution of the relativistic and non-relativistic wave equations for central potentials has attracted enormous interest in recent years. By using the basic Nikiforov-Uvarov quantum mechanical concepts and formalism, the energy eigenvalue equations and the corresponding wave functions of the Klein–Gordon and Schrodinger equations with the interaction of Modified Hylleraas-Hulthen Potentials (MHHP) were obtained using the conventional Pekeris-type approximation scheme to the orbital centrifugal term. The corresponding unnormalized eigen functions are evaluated in terms of Jacobi polynomials.

Spinless relativistic particle in energy-dependent potential and normalization of the wave function

Open Physics ◽  
2014 ◽  
Vol 12 (6) ◽  
Author(s):  
Amar Benchikha ◽  
Lyazid Chetouani
Keyword(s):  
Wave Function ◽  
Spectral Decomposition ◽  
Relativistic Particle ◽  
Wave Functions ◽  
Integral Approach ◽  
Normalizing Constant ◽  
Klein Gordon ◽  
Dependent Potential ◽  
Energy Dependent ◽  
Coulomb Potentials

AbstractThe problem of normalization related to a Klein-Gordon particle subjected to vector plus scalar energy-dependent potentials is clarified in the context of the path integral approach. In addition the correction relating to the normalizing constant of wave functions is exactly determined. As examples, the energy dependent linear and Coulomb potentials are considered. The wave functions obtained via spectral decomposition, were found exactly normalized.

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