THE ASYMPTOTIC ITERATION METHOD FOR DIRAC AND KLEIN–GORDON EQUATIONS WITH A LINEAR SCALAR POTENTIAL

2006 ◽  
Vol 21 (19n20) ◽  
pp. 4127-4135 ◽  
Author(s):  
T. BARAKAT
Keyword(s):  
Iteration Method ◽  
Bound States ◽  
Scalar Potential ◽  
Asymptotic Iteration Method ◽  
Klein Gordon ◽  
Linear Scalar

The asymptotic iteration method is used for Dirac and Klein–Gordon equations with a linear scalar potential to obtain the relativistic eigenenergies. A parameter, ς = 0, 1, is introduced in such a way that one can obtain Klein–Gordon bound states from Dirac bound states. It is shown that this method asymptotically gives accurate results for both Dirac and Klein–Gordon equations.

Nonrelativistic and relativistic bound state solutions of the molecular Tietz potential via the improved asymptotic iteration method

2014 ◽  
Vol 92 (3) ◽  
pp. 215-220 ◽  
Author(s):  
W.A. Yahya ◽  
K. Issa ◽  
B.J. Falaye ◽  
K.J. Oyewumi
Keyword(s):  
Iteration Method ◽  
Vibrational Energy ◽  
Bound State ◽  
Asymptotic Iteration Method ◽  
Quantum Numbers ◽  
Approximate Analytical Solutions ◽  
Relative Closeness ◽  
Klein Gordon ◽  
Tietz Potential ◽  
Schrödinger System

We have obtained the approximate analytical solutions of the relativistic and nonrelativistic molecular Tietz potential using the improved asymptotic iteration method. By approximating the centrifugal term through the Greene–Aldrich approximation scheme, we have obtained the energy eigenvalues and wave functions for all orbital quantum numbers [Formula: see text]. Where necessary, we made comparison with the result obtained previously in the literature. The relative closeness of the two results reveal the accuracy of the method presented in this study. We proceed further to obtain the rotational-vibrational energy spectrum for some diatomic molecules. These molecules are CO, HCl, H2, and LiH. We have also obtained the relativistic bound state solution of the Klein−Gordon equation with this potential. In the nonrelativistic limits, our result converges to that of the Schrödinger system.

scholarly journals Generalized relativistic wave equations with intrinsic maximum momentum

2014 ◽  
Vol 29 (15) ◽  
pp. 1450080 ◽  
Author(s):  
Chee Leong Ching ◽  
Wei Khim Ng
Keyword(s):  
Bound States ◽  
Wave Equations ◽  
Scalar Potential ◽  
Bound State ◽  
Relativistic Wave Equations ◽  
Wave Functions ◽  
Relativistic Wave ◽  
One Dimensional ◽  
Nonperturbative Effect ◽  
Klein Gordon

We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wave functions of one-dimensional Klein–Gordon and Dirac equation with linear confining potentials, and the Dirac oscillator. Bound state solutions are only possible when the strength of scalar potential is stronger than vector potential. The energy spectrum of the systems studied is bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have future applications.

scholarly journals Effects of Kaluza-Klein Theory and Potential on a Generalized Klein-Gordon Oscillator in the Cosmic String Space-Time

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Cosmic String ◽  
Bound States ◽  
Scalar Potential ◽  
Space Time ◽  
Relativistic Energy ◽  
Klein Theory ◽  
Klein Gordon ◽  
Coulomb Type ◽  
Relativistic Analogue ◽  
Kaluza Klein

In this paper, we solve a generalized Klein-Gordon oscillator in the cosmic string space-time with a scalar potential of Cornell-type within the Kaluza-Klein theory and obtain the relativistic energy eigenvalues and eigenfunctions. We extend this analysis by replacing the Cornell-type with Coulomb-type potential in the magnetic cosmic string space-time and analyze a relativistic analogue of the Aharonov-Bohm effect for bound states.

scholarly journals Spin-0 scalar particle interacts with scalar potential in the presence of magnetic field and quantum flux under the effects of KKT in 5D cosmic string spacetime

2020 ◽  
pp. 2150004
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Magnetic Field ◽  
Quantum Dynamics ◽  
Bound States ◽  
Relativistic Quantum ◽  
Energy Levels ◽  
Scalar Potential ◽  
Scalar Particle ◽  
Klein Theory ◽  
Klein Gordon ◽  
Quantum Flux

In this paper, we study a relativistic quantum dynamics of spin-0 scalar particle interacts with scalar potential in the presence of a uniform magnetic field and quantum flux in background of Kaluza–Klein theory (KKT). We solve Klein–Gordon equation in the considered framework and analyze the relativistic analogue of the Aharonov–Bohm effect for bound states. We show that the energy levels depend on the global parameters characterizing the spacetime, scalar potential and the magnetic field which break their degeneracy.

Studying novel 1D potential via the AIM

2021 ◽  
pp. 2150141
Author(s):  
A. J. Sous
Keyword(s):  
Iteration Method ◽  
Bound States ◽  
Small Deformation ◽  
Asymptotic Iteration Method ◽  
Finite Spectrum ◽  
Deformation Limit ◽  
Potential Parameters

In this work, we would like to apply the asymptotic iteration method (AIM) to a newly proposed Morse-like deformed potential introduced recently by Assi, Alhaidari and Bahlouli.[Formula: see text] This interesting potential can support bound states and/or resonances. However, in this work, we are only interested in bound states. We considered several choices of the potential parameters and obtained the associated spectrum. Finally, we study the small deformation limit at which this finite spectrum system will transition to infinite spectrum size.

scholarly journals Aharonov–Bohm effect for bound states in relativistic scalar particle systems in a spacetime with a spacelike dislocation

2018 ◽  
Vol 27 (02) ◽  
pp. 1850005 ◽  
Author(s):  
R. L. L. Vitória ◽  
K. Bakke
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Bound States ◽  
Topological Defect ◽  
Scalar Potential ◽  
Hard Wall ◽  
Wall Potential ◽  
Bohm Effect ◽  
Aharonov Bohm ◽  
Linear Scalar

We investigate the analog effect of the Aharonov–Bohm effect for bound states in two relativistic quantum systems in a spacetime with a spacelike dislocation. We assume that the topological defect has an internal magnetic flux. Then, we analyze the interaction of a charged particle with a uniform magnetic field in this topological defect spacetime, and thus, we extend this analysis to the confinement of a hard-wall potential and a linear scalar potential. Later, the interaction of the Klein–Gordon oscillator with a uniform magnetic field is analyzed. We first focus on the effects of torsion that stem from the spacetime with a spacelike dislocation and the geometric quantum phase. Then, we analyze the effects of torsion and the geometric quantum phase under the presence of a hard-wall potential and a linear scalar potential.

Central potential effects induced by Lorentz symmetry violation on modified quantum oscillator field

2022 ◽  
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Bound States ◽  
Quantum Effect ◽  
Scalar Potential ◽  
Lorentz Symmetry ◽  
Quantum Oscillator ◽  
Standard Model Extension ◽  
Symmetry Violation ◽  
Quantum Numbers ◽  
Model Extension ◽  
Klein Gordon

In this paper, effects of Lorentz symmetry violation determined by a tensor field [Formula: see text] out of the Standard Model Extension on a modified quantum oscillator field in the presence of Cornell-type scalar potential are analyzed. We first introduced a scalar potential [Formula: see text] by modifying the mass square term via transformation [Formula: see text] in the Klein–Gordon equation, and then replace the momentum operator [Formula: see text], where [Formula: see text] is an arbitrary function other than [Formula: see text] to study the modified Klein–Gordon oscillator. We solve the wave equation and obtain the analytical bound-states solutions and see the dependence of oscillator frequency [Formula: see text] on the quantum numbers [Formula: see text] as well as on Lorentz-violating parameters with the potential which shows a quantum effect.

scholarly journals Closed-form solutions for the Schrödinger wave equation with non-solvable potentials: A perturbation approach

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 208-214
Author(s):  
Haifa Ibrahim Alrebdi ◽  
Thabit Barakat
Keyword(s):  
Wave Equation ◽  
Closed Form ◽  
Bound States ◽  
Perturbation Technique ◽  
Scalar Potential ◽  
Asymptotic Iteration Method ◽  
Perturbation Approach ◽  
Closed Form Solutions ◽  
Solvable Potential ◽  
Unperturbed Problem

Abstract To obtain closed-form solutions for the radial Schrödinger wave equation with non-solvable potential models, we use a simple, easy, and fast perturbation technique within the framework of the asymptotic iteration method (PAIM). We will show how the PAIM can be applied directly to find the analytical coefficients in the perturbation series, without using the base eigenfunctions of the unperturbed problem. As an example, the vector Coulomb ( ∼ 1 / r ) \left( \sim 1\hspace{0.1em}\text{/}\hspace{0.1em}r) and the harmonic oscillator ( ∼ r 2 ) \left( \sim {r}^{2}) plus linear ( ∼ r ) \left( \sim r) scalar potential parts implemented with their counterpart spin-dependent terms are chosen to investigate the meson sectors including charm and beauty quarks. This approach is applicable in the same form to both the ground state and the excited bound states and can be easily applied to other strongly non-solvable potential problems. The procedure of this method and its results will provide a valuable hint for investigating tetraquark configuration.

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