Analytical study of D-dimensional fractional Klein–Gordon equation with a fractional vector plus a scalar potential

Pramana ◽  
2020 ◽  
Vol 94 (1) ◽  
Author(s):  
Tapas Das ◽  
Uttam Ghosh ◽  
Susmita Sarkar ◽  
Shantanu Das
Keyword(s):  
Analytical Study ◽  
Gordon Equation ◽  
Scalar Potential ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals Bound State Solutions of Three-Dimensional Klein-Gordon Equation for Two Model Potentials by NU Method

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
N. Tazimi ◽  
A. Ghasempour
Keyword(s):  
Gordon Equation ◽  
Scalar Potential ◽  
Laguerre Polynomials ◽  
Three Dimensional ◽  
Bound State ◽  
Molecular Systems ◽  
Klein Gordon ◽  
Linear Differential ◽  
Nu Method ◽  
Klein Gordon Equation

In this study, we investigate the relativistic Klein-Gordon equation analytically for the Deng-Fan potential and Hulthen plus Eckart potential under the equal vector and scalar potential conditions. Accordingly, we obtain the energy eigenvalues of the molecular systems in different states as well as the normalized wave function in terms of the generalized Laguerre polynomials function through the NU method, which is an effective method for the exact solution of second-order linear differential equations.

scholarly journals Relativistic scalar particle subject to a confining potential and Lorentz symmetry breaking effects in the cosmic string space–time

2016 ◽  
Vol 31 (07) ◽  
pp. 1650026 ◽  
Author(s):  
H. Belich ◽  
K. Bakke
Keyword(s):  
Symmetry Breaking ◽  
Cosmic String ◽  
Gordon Equation ◽  
Scalar Potential ◽  
Scalar Particle ◽  
Lorentz Symmetry ◽  
Space Time ◽  
Klein Gordon ◽  
Lorentz Symmetry Breaking ◽  
Klein Gordon Equation

The behavior of a relativistic scalar particle subject to a scalar potential under the effects of the violation of the Lorentz symmetry in the cosmic string space–time is discussed. It is considered two possible scenarios of the Lorentz symmetry breaking in the CPT-even gauge sector of the Standard Model Extension defined by a tensor [Formula: see text]. Then, by introducing a scalar potential as a modification of the mass term of the Klein–Gordon equation, it is shown that the Klein–Gordon equation in the cosmic string space–time is modified by the effects of the Lorentz symmetry violation backgrounds and bound state solution to the Klein–Gordon equation can be obtained.

THE KLEIN–GORDON EQUATION WITH A COULOMB PLUS SCALAR POTENTIAL IN D DIMENSIONS

2004 ◽  
Vol 13 (03) ◽  
pp. 597-610 ◽  
Author(s):  
ZHONG-QI MA ◽  
SHI-HAI DONG ◽  
XIAO-YAN GU ◽  
JIANG YU ◽  
M. LOZADA-CASSOU
Keyword(s):  
Angular Momentum ◽  
Quantum Number ◽  
Coulomb Potential ◽  
Gordon Equation ◽  
Scalar Potential ◽  
Positive Energy ◽  
Angular Momentum Quantum Number ◽  
Klein Gordon ◽  
Klein Gordon Equation

The solutions of the Klein–Gordon equation with a Coulomb plus scalar potential in D dimensions are exactly obtained. The energy E(n,l,D) is analytically presented and the dependence of the energy E(n,l,D) on the dimension D is analyzed in some detail. The positive energy E(n,0,D) first decreases and then increases with increasing dimension D. The positive energy E(n,l D)(l≠0) increases with increasing dimension D. The dependences of the negative energies E(n,0,D) and E(n,l,D)(l≠0) on the dimension D are opposite to those of the corresponding positive energies E(n,0,D) and E(n,l,D)(l≠0). It is found that the energy E(n,0,D) is symmetric with respect to D=2 for D∈(0,4). It is also found that the energy E(n,l,D)(l≠0) is almost independent of the angular momentum quantum number l for large D and is completely independent of the angular momentum quantum number l if the Coulomb potential is equal to the scalar one. The energy E(n,l D) is almost overlapping for large D.

Relativistic quantum motion of spin-0 particles with a Cornell-type potential in (1 + 2)-dimensional Gürses spacetime backgrounds

2019 ◽  
Vol 34 (38) ◽  
pp. 1950314 ◽  
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Quantum Dynamics ◽  
Gordon Equation ◽  
Relativistic Quantum ◽  
Scalar Potential ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Klein Gordon ◽  
Quantum Motion ◽  
Type Potential ◽  
Klein Gordon Equation

In this work, we investigate the relativistic quantum dynamics of spin-0 particles in the background of (1 + 2)-dimensional Gürses spacetime [M. Gürses, Class. Quantum Grav. 11, 2585 (1994)] with interactions. We solve the Klein–Gordon equation subject to Cornell-type scalar potential in the considered framework, and evaluate the energy eigenvalues and corresponding wave functions, in detail.

scholarly journals Bound state solutions of the Klein–Gordon equation with energy-dependent potentials

2020 ◽  
pp. 2150016
Author(s):  
B. C. Lütfüoğlu ◽  
A. N. Ikot ◽  
M. Karakoc ◽  
G. T. Osobonye ◽  
A. T. Ngiangia ◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Gordon Equation ◽  
Scalar Potential ◽  
Bound State ◽  
Asymptotic Iteration Method ◽  
Equal Sign ◽  
Tuning Parameters ◽  
Klein Gordon ◽  
Energy Dependent ◽  
Klein Gordon Equation

In this paper, we investigate the exact bound state solution of the Klein–Gordon equation for an energy-dependent Coulomb-like vector plus scalar potential energies. To the best of our knowledge, this problem is examined in literature with a constant and position dependent mass functions. As a novelty, we assume a mass-function that depends on energy and position and revisit the problem with the following cases: First, we examine the case where the mixed vector and scalar potential energy possess equal magnitude and equal sign as well as an opposite sign. Then, we study pure scalar and pure vector cases. In each case, we derive an analytic expression of the energy spectrum by employing the asymptotic iteration method. We obtain a nontrivial relation among the tuning parameters which lead the examined problem to a constant mass one. Finally, we calculate the energy spectrum by the Secant method and show that the corresponding unnormalized wave functions satisfy the boundary conditions. We conclude the paper with a comparison of the calculated energy spectra versus tuning parameters.

scholarly journals Sharp comparison theorems for the Klein–Gordon equation in d dimensions

2016 ◽  
Vol 25 (06) ◽  
pp. 1650039 ◽  
Author(s):  
Richard L. Hall ◽  
Petr Zorin
Keyword(s):  
Gordon Equation ◽  
Scalar Potential ◽  
Variable Mass ◽  
Comparison Theorems ◽  
Time Component ◽  
Klein Gordon ◽  
Klein Gordon Equation

We establish sharp (or ’refined’) comparison theorems for the Klein–Gordon equation. We show that the condition [Formula: see text], which leads to [Formula: see text], can be replaced by the weaker assumption [Formula: see text] which still implies the spectral ordering [Formula: see text]. In the simplest case, for [Formula: see text], [Formula: see text], [Formula: see text] or [Formula: see text] and for [Formula: see text], [Formula: see text], [Formula: see text] or [Formula: see text]. We also consider sharp comparison theorems in the presence of a scalar potential [Formula: see text] (a ‘variable mass’) in addition to the vector term [Formula: see text] (the time component of a four-vector). The theorems are illustrated by a variety of explicit detailed examples.

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