scholarly journals Relativistic solution in D-dimensions to a spin-zero particle for equal scalar and vector ring-shaped Kratzer potential

Open Physics ◽  
2008 ◽  
Vol 6 (1) ◽  
Author(s):  
Sameer Ikhdair ◽  
Ramazan Sever
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Wave Functions ◽  
Three Dimensions ◽  
Vector Potentials ◽  
Klein Gordon ◽  
Energy Bound ◽  
Uvarov Method ◽  
Equal Scalar ◽  
Exact Energy

AbstractThe Klein-Gordon equation in D-dimensions for a recently proposed ring-shaped Kratzer potential is solved analytically by means of the conventional Nikiforov-Uvarov method. The exact energy bound states and the corresponding wave functions of the Klein-Gordon are obtained in the presence of the non-central equal scalar and vector potentials. The results obtained in this work are more general and can be reduced to the standard forms in three dimensions given by other works.

EXACT SOLUTIONS OF THE KLEIN–GORDON EQUATION FOR THE ROSEN–MORSE TYPE POTENTIALS VIA NIKIFOROV–UVAROV METHOD

2008 ◽  
Vol 23 (35) ◽  
pp. 3005-3013 ◽  
Author(s):  
A. REZAEI AKBARIEH ◽  
H. MOTAVALI
Keyword(s):  
Exact Solutions ◽  
Gordon Equation ◽  
Bound State ◽  
S Wave ◽  
Vector Potentials ◽  
Klein Gordon ◽  
The One ◽  
Uvarov Method ◽  
Equal Scalar ◽  
Klein Gordon Equation

The exact solutions of the one-dimensional Klein–Gordon equation for the Rosen–Morse type potential with equal scalar and vector potentials are presented. First, we briefly review Nikiforov–Uvarov mathematical method. Using this method, wave functions and corresponding exact energy equation are obtained for the s-wave bound state. It has been shown that the results for Rosen–Morse type potentials reduce to the standard Rosen–Morse well and Eckart potentials in the special case. The PT-symmetry for these potentials is also considered.

scholarly journals EXACT SOLUTIONS OF THE MODIFIED KRATZER POTENTIAL PLUS RING-SHAPED POTENTIAL IN THE D-DIMENSIONAL SCHRÖDINGER EQUATION BY THE NIKIFOROV–UVAROV METHOD

2008 ◽  
Vol 19 (02) ◽  
pp. 221-235 ◽  
Author(s):  
SAMEER M. IKHDAIR ◽  
RAMAZAN SEVER
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound States ◽  
Laguerre Polynomials ◽  
Three Dimensional ◽  
Wave Functions ◽  
Modified Kratzer Potential ◽  
Energy Bound ◽  
Uvarov Method ◽  
Exact Energy

We present analytically the exact energy bound-states solutions of the Schrödinger equation in D dimensions for a recently proposed modified Kratzer plus ring-shaped potential by means of the Nikiforov–Uvarov method. We obtain an explicit solution of the wave functions in terms of hyper-geometric functions (Laguerre polynomials). The results obtained in this work are more general and true for any dimension which can be reduced to the well-known three-dimensional forms given by other works.

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.

Exact treatment of the relativistic double ring-shaped Kratzer potential using the quantum Hamilton–Jacobi formalism

2015 ◽  
Vol 30 (16) ◽  
pp. 1550082 ◽  
Author(s):  
A. Gharbi ◽  
S. Touloum ◽  
A. Bouda
Keyword(s):  
Gordon Equation ◽  
Relativistic Quantum ◽  
Separable Potential ◽  
Relativistic Energy ◽  
Double Ring ◽  
Vector Potentials ◽  
Jacobi Formalism ◽  
Klein Gordon ◽  
Equal Scalar ◽  
Hamilton Jacobi Equation

We study the Klein–Gordon equation with noncentral and separable potential under the condition of equal scalar and vector potentials and we obtain the corresponding relativistic quantum Hamilton–Jacobi equation. The application of the quantum Hamilton–Jacobi formalism to the double ring-shaped Kratzer potential leads to its relativistic energy spectrum as well as the corresponding eigenfunctions.

Klein–Gordon Solutions for a Yukawa-like Potential

2013 ◽  
Vol 68 (12) ◽  
pp. 715-724 ◽  
Author(s):  
Sameer M. Ikhdair ◽  
Majid Hamzavi
Keyword(s):  
Vector Potential ◽  
Gordon Equation ◽  
Wave Functions ◽  
Potential Fields ◽  
Energy Eigenvalues ◽  
Exact Agreement ◽  
Klein Gordon ◽  
Uvarov Method ◽  
Type Potential ◽  
Klein Gordon Equation

The Klein-Gordon equation for a recently proposed Yukawa-type potential is solved with any orbital quantum number l. In the equally mixed scalar-vector potential fields S(r) = ±V(r), the approximate energy eigenvalues and their wave functions for a particle and anti-particle are obtained by means of the parametric Nikiforov-Uvarov method. The non-relativistic solutions are also investigated. It is found that the present analytical results are in exact agreement with the previous ones.

Sign in / Sign up

Export Citation Format

Share Document