On localized long-lived three-dimensional solutions of the nonlinear Klein-Gordon equation with a fractional power potential

JETP Letters ◽  
2014 ◽  
Vol 100 (7) ◽  
pp. 477-480 ◽  
Author(s):  
E. G. Ekomasov ◽  
R. K. Salimov
Keyword(s):  
Gordon Equation ◽  
Three Dimensional ◽  
Fractional Power ◽  
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 The geometric origin of Lie point symmetries of the Schrödinger and the Klein–Gordon equations

2014 ◽  
Vol 11 (04) ◽  
pp. 1450037 ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Michael Tsamparlis
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Gordon Equation ◽  
Three Dimensional ◽  
Lie Point Symmetries ◽  
Geometric Origin ◽  
Klein Gordon ◽  
Klein Gordon Equation

We determine the Lie point symmetries of the Schrödinger and the Klein–Gordon equations in a general Riemannian space. It is shown that these symmetries are related with the homothetic and the conformal algebra of the metric of the space, respectively. We consider the kinematic metric defined by the classical Lagrangian and show how the Lie point symmetries of the Schrödinger equation and the Klein–Gordon equation are related with the Noether point symmetries of this Lagrangian. The general results are applied to two practical problems: (a) The classification of all two- and three-dimensional potentials in a Euclidean space for which the Schrödinger equation and the Klein–Gordon equation admit Lie point symmetries; and (b) The application of Lie point symmetries of the Klein–Gordon equation in the exterior Schwarzschild spacetime and the determination of the metric by means of conformally related Lagrangians.

Nonhomogeneous three-dimensional structures described by the nonlinear Klein–Gordon equation

1990 ◽  
Vol 68 (9) ◽  
pp. 756-759 ◽  
Author(s):  
M. Otwinowski ◽  
R. Paul ◽  
J. A. Tuszynski
Keyword(s):  
Exact Solutions ◽  
Critical Point ◽  
Gordon Equation ◽  
Three Dimensional ◽  
Vortex Rings ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Klein Gordon ◽  
Klein Gordon Equation

We present exact solutions to the nonlinear Klein–Gordon equation in (3 + 1) dimensions. Vortex rings, spirals, and other solutions are demonstrated. On the basis of our solutions we discuss various nonhomogeneous patterns, which can be formed at the critical point of systems described by the Ginzburg–Landau model.

scholarly journals EXACT BOUND STATES OF THE D-DIMENSIONAL KLEIN–GORDON EQUATION WITH EQUAL SCALAR AND VECTOR RING-SHAPED PSEUDOHARMONIC POTENTIAL

2008 ◽  
Vol 19 (09) ◽  
pp. 1425-1442 ◽  
Author(s):  
SAMEER M. IKHDAIR ◽  
RAMAZAN SEVER
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Energy Levels ◽  
Three Dimensional ◽  
Bound State ◽  
Exact Bound ◽  
Pseudoharmonic Potential ◽  
Klein Gordon ◽  
Equal Scalar ◽  
Klein Gordon Equation

We present the exact solution of the Klein–Gordon equation in D-dimensions in the presence of the equal scalar and vector pseudoharmonic potential plus the ring-shaped potential using the Nikiforov–Uvarov method. We obtain the exact bound state energy levels and the corresponding eigen functions for a spin-zero particles. We also find that the solution for this ring-shaped pseudoharmonic potential can be reduced to the three-dimensional (3D) pseudoharmonic solution once the coupling constant of the angular part of the potential becomes zero.

The Klein–Gordon equation with modified Coulomb plus inverse-square potential in the noncommutative three-dimensional space

2019 ◽  
Vol 35 (05) ◽  
pp. 2050015 ◽  
Author(s):  
Abdelmadjid Maireche
Keyword(s):  
Gordon Equation ◽  
Dimensional Space ◽  
Star Product ◽  
Three Dimensional ◽  
Real Space ◽  
Vector Potentials ◽  
State Formula ◽  
Klein Gordon ◽  
Equal Scalar ◽  
Klein Gordon Equation

The Klein–Gordon equation with equal scalar and vector potentials [Formula: see text] describing the dynamics of a three-dimensional under the modified Coulomb plus inverse-square potential is considered, in the symmetries of noncommutative quantum mechanics (NCQM), using Bopp’s shift method. The new energy of [Formula: see text]th excited state [Formula: see text] is obtained as a function of the shift energy [Formula: see text] and [Formula: see text] is obtained via first-order perturbation theory in the three-dimensional noncommutative real space (NC: 3D-RS) symmetries instead of solving modified Klein–Gordon equation (MKGE) with the Weyl–Moyal star product. It is found that the perturbative solutions of discrete spectrum depended by the Gamma function, the discreet atomic quantum numbers [Formula: see text] and the potential parameters (A and B), in addition to noncommutativity parameters ([Formula: see text] and [Formula: see text]), which are induced with the effect of (space–space) noncommutativity properties.

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