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.

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.

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.

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.

BILINEAR FORM AND SOLITON SOLUTIONS FOR THE COUPLED NONLINEAR KLEIN–GORDON EQUATIONS

2012 ◽  
Vol 26 (15) ◽  
pp. 1250057
Author(s):  
HE LI ◽  
XIANG-HUA MENG ◽  
BO TIAN
Keyword(s):  
Field Theory ◽  
Bilinear Form ◽  
Gordon Equation ◽  
Relativistic Quantum ◽  
Soliton Solutions ◽  
Relativistic Quantum Mechanics ◽  
Klein Gordon ◽  
Truncated Painlevé Expansion ◽  
Klein Gordon Equation ◽  
Singular Manifolds

With the coupling of a scalar field, a generalization of the nonlinear Klein–Gordon equation which arises in the relativistic quantum mechanics and field theory, i.e., the coupled nonlinear Klein–Gordon equations, is investigated via the Hirota method. With the truncated Painlevé expansion at the constant level term with two singular manifolds, the coupled nonlinear Klein–Gordon equations are transformed to a bilinear form. Starting from the bilinear form, with symbolic computation, we obtain the N-soliton solutions for the coupled nonlinear Klein–Gordon equations.

scholarly journals Solution of Q-Deformed D-Dimensional Klein-Gordon Equation Kratzer Potential using Hypergeometric Method

2019 ◽  
Vol 9 (2) ◽  
pp. 163
Author(s):  
Suparmi Suparmi ◽  
Dyah Ayu Dianawati ◽  
Cari Cari
Keyword(s):  
Gordon Equation ◽  
Energy Levels ◽  
Spin Symmetry ◽  
Relativistic Energy ◽  
Dimensional Parameter ◽  
Energy Value ◽  
Quantum Numbers ◽  
Klein Gordon ◽  
Dimensional Parameters ◽  
Klein Gordon Equation

The Q-deformed D-dimensional Klein Gordon equation with Kratzer potential is solved by using Hypergeometric method in the case of exact spin symmetry. The linear radial momentum of D-dimensional Klein Gordon equation is disturbed by the presence of the quadratic radial posisiton. The Klein-Gordon D-dimensional equation is reduced to one-dimensional Schrodinger like equation with variable substitution. The solution of the D-dimensional Klein-Gordon equation is determined in the form of a general equation of the Hypergeometry function using the Kratzer potential variable and the quantum deformation variable. From this equation, relativistic energy and wave function are determined. In addition, the relativistic energy equation can be used to calculate numerical energy levels for diatomic particles (CO, NO, O2) using Matlab R2013a software. The results obtained show that the q-deformed quantum parameters, quantum numbers and dimensions affect the value of relativistic energy for zero-pin particles. The value of energy increases with increasing value of quantum number n, q-deformed parameters, and d-dimensional parameters. Of the three parameters, q-deformed parameter is the most dominant to give change in energy value; the increasing q-deformed parameter causes the energy value increases significantly compared to the d-dimensional parameter and quantum numbers n.

scholarly journals The Klein-Gordon equation with the Kratzer potential in d dimensions

Open Physics ◽  
2008 ◽  
Vol 6 (3) ◽  
Author(s):  
Nasser Saad ◽  
Richard Hall ◽  
Hakan Ciftci
Keyword(s):  
Exact Solutions ◽  
Gordon Equation ◽  
Monic Polynomial ◽  
Bound State ◽  
Asymptotic Iteration Method ◽  
Vector Potentials ◽  
Klein Gordon ◽  
Elementary Symmetric Polynomials ◽  
Potential Parameters ◽  
Klein Gordon Equation

AbstractWe apply the Asymptotic Iteration Method to obtain the bound-state energy spectrum for the d-dimensional Klein-Gordon equation with scalar S(r) and vector potentials V(r). When S(r) and V(r) are both Coulombic, we obtain all the exact solutions; when the potentials are both of Kratzer type, we obtain all the exact solutions for S(r) = V(r); if S(r) > V(r) we obtain exact solutions under certain constraints on the potential parameters: in this case, a possible general solution is found in terms of a monic polynomial, whose coefficients form a set of elementary symmetric polynomials.

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