D-dimensional Klein-Gordon Equation Research Articles

[formula omitted]-dimensional Klein–Gordon equation in presence of deformed generalized Deng–Fan with Yukawa potential class: Approximate bound state solutions in relativistic and non-relativistic regimes

In this paper, we examine the bound state solutions of the D-dimensional Klein–Gordon equation for a deformed Deng–Fan potential in generalized form along with Yukawa potential class. The supersymmetric quantum mechanics method and Nikiforov–Uvarov method are employed, utilizing a proper correspondence to the centrifugal potential term. Remarkably, in both methods, we obtain the same analytical expressions for normalized wave functions and energy eigenvalues, expressed in closed form by hypergeometric functions and Jacobi polynomials, for all l and n quantum states. Additionally, we explore the thermodynamic quantities (internal energy, partition function, specific heat, entropy and free energy) in case of both relativistic and non-relativistic regimes for the aforementioned potential. Finally, we demonstrate energy variation against various potential parameters for a few diatomic molecules pictorially.

Analytical Solutions of the D-dimensional Klein-Gordon equation with q-deformed modified P¨oschl-Teller Potential

In this article, the D-dimensional Klein-Gordon equation within the framework of Greene-Aldrich approximations scheme for q-deformed modified P¨oschl-Teller Potential is solved for s-wave and arbitrary angular momenta. The energy eigenvalues and corresponding wave functions are obtained in an exact analytical manner via the Nikiforov-Uvarov (N-U) method. Further, it is shown that in the non-relativistic limit, the energy eigenvalues reduce to that of Schrodinger equations for the potential. It is also shown that, the obtained results lead to the solutions of the same problem for modified P¨oschl-Teller potential for \(q = 1\).

The Klein–Gordon equation with equal scalar and vector Bargmann potentials in [formula omitted] dimensions

Using an improved Greene-Aldrich approximation scheme to handle the centrifugal potential, we solve the D-dimensional Klein–Gordon equation with equal scalar and vector Bargmann potentials with a non-zero angular momentum number. The equation giving the bound-state energy eigenvalues as well as the corresponding normalized radial wave functions are obtained. The particular cases of Hultén and Yukawa potentials are also discussed. A lower-bound for the energy levels is obtained and their behaviour with the parameters of the Bargmann potential is analysed.

Analytical solutions of D-dimensional Klein–Gordon equation with modified Mobius squared potential

Approximate solutions of Klein–Gordon equation are obtained for the modified Mobius squared potential using the Nikiforov-Uvarov (NU) method. The relativistic energy eigenvalues and corresponding wave functions are obtained. It is further shown that in the non-relativistic limit, the energy eigenvalues reduces to that of Schrodinger equation. The behavior of CO, NO and HCl molecules are investigated subject to the modified Mobius squared potential. Numerical values of the energies of these diatomic molecules are also presented for arbitrary values of quantum numbers n and l. Finally, plots showing the variation of the energy against various potential parameters are presented for the selected diatomic molecules.

Approximate solutions of D-dimensional Klein–Gordon equation with Yukawa potential via Nikiforov–Uvarov method

In this work, we obtain the Klein–Gordon equation solutions for the Yukawa potential using the Nikiforov–Uvarov method. The energy eigenvalues are obtained both in relativistic and non-relativistic regime. The corresponding eigenfunction are obtained in terms of Laguerre polynomial. We applied the present results to calculate heavy-meson masses of charmonium $$ c\bar{c} $$ and bottomonium $$ b\bar{b} $$ , and we got the numerical values for states 1S–1F. The results are in good agreement with experimental data and the work of other researchers.

Eigensolution and various properties of the screened cosine Kratzer potential in D dimensions via relativistic and non-relativistic treatment

In this article, we proposed screened cosine Kratzer potential (SCKP). Using approximation suggested by Greene–Aldrich, the approximate bound-state solutions of the D-dimensional Klein–Gordon equation for SCKP have been obtained via the generalized Nikiforov–Uvarov method. The bound-state energy eigenvalues and the corresponding normalized wave functions expressed in terms of hypergeometric functions were obtained. From the proposed SCKP model, we recovered different potentials such as screened Kratzer potential, standard Kratzer potential, generalized cosine Yukawa potential, screened Coulomb potential, Coulomb potential, inversely quadratic Yukawa potential and its corresponding energy eigenvalues from obtained energy eigenvalues of the SCKP in both the relativistic and non-relativistic regime. We obtained rotational–vibrational energy for few heterogeneous (LiH, HCl, NO) and homogeneous (H $$_2$$ , I $$_2$$ , O $$_2$$ ) diatomic molecules in three dimensions. The numerical results obtained for LiH, HCl, NO and I $$_2$$ , O $$_2$$ diatomic molecules are in very good agreement with the results previously obtained by others. We obtained various properties of the SCKP such as thermodynamical properties (partition function, vibrational mean energy, vibrational mean free energy, vibrational specific heat capacity and vibrational entropy, information energy $$E(\gamma )$$ , Tsallis entropy T(q), Renyi entropy R(q), Shannon entropy $$ S(\gamma )$$ and Fisher information entropy $$I(\gamma )$$ ) using energy eigenvalues and eigenfunctions, the expressions for the expectation values of the square of inverse of position $$1/r^2$$ , inverse of position 1/r, kinetic energy T, and square of momentum $$p^2$$ via Hellmann–Feynman theorem. We also presented quarkonium mass spectroscopy using energy eigenvalues of the SCKP.

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

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.

Spatially q-deformed radial momentum of d-dimensional Klein-Gordon equation for Harmonic Oscillator plus Inverse Quadratic potential investigated using hypergeometric method

Spatially quadratic deformation radial momentum of D-dimensional Klein-Gordon equation with three-dimensional Harmonic Oscillator and Inverse Quadratic potential was investigated using Hypergeometric Method. By using appropriate variable transformation, D-Dimensional Klein-Gordon equation for q deformed momentum was reduced into one order dimensional Schrodinger like equation with Pöschl-Teller like potential. The relativistic energy and wave function equations were obtained from the solution of Schrodinger like equation. Then, the relativistic energy and wave function were calculated and visualized using Matlab R2013 software, respectively. The q deformed parameter had the effect to the relativistic energy and wave function. The increase of q deformed parameter causes the increase of energy spectra and the decrease of amplitude.

D-dimensional Klein-Gordon equation with spatially q-deformed of radial momentum for Kratzer potential analyzed by using hypergeometric method

Hypergeometric method can be used to solve D-dimensional Klein-Gordon equation with q-deformed of radial momentum for Kratzer potential. By substituting q-deformed of radial momentum variable, the D-dimensional and the potential parameters to obtain the second order of D-dimensional Klein-Gordon equation which is used to determine the energy and wave function equations. The analytical result of energy can be founded with D-dimension and q-deformed of radial momentum variations. As a result, the rise of D-dimension values cause the rise of energy values, while the rice of q deformation values causes the decline of energy values.

Asymptotic iteration method for solution of the Kratzer potential in D-dimensional Klein-Gordon equation

The solution of D-dimensional Klein-Gordon equation for Kratzer potential was presented using asymptotic iteration method. The D-dimensional Klein-Gordon equation was reduced to one-dimensional radial differential equation. The Kratzer central potential was used in radial part solution to obtain the energy eigenvalues and radial wave function. The bound-state energy eigenvalues were calculated for various values of quantum numbers and dimensions using Matlab software.

New solutions of the [formula omitted]-dimensional Klein–Gordon equation via mapping onto the nonrelativistic one-dimensional Morse potential

New exact analytical bound-state solutions of the D-dimensional Klein–Gordon equation for a large set of couplings and potential functions are obtained via mapping onto the nonrelativistic bound-state solutions of the one-dimensional generalized Morse potential. The eigenfunctions are expressed in terms of generalized Laguerre polynomials, and the eigenenergies are expressed in terms of solutions of irrational equations at the worst. Several analytical results found in the literature, including the so-called Klein–Gordon oscillator, are obtained as particular cases of this unified approach.

Bound state solutions of D-dimensional Klein–Gordon equation with hyperbolic potential

By using the basic supersymmetric quantum mechanics concepts and formalism, the energy eigenvalue equation and the corresponding wave function of the Klein–Gordon equation with vector and scalar potentials for an arbitrary dimensions are obtained together with hyperbolic potential using a suitable approximation scheme to the orbital centrifugal term. The non-relativistic limit is obtained and the numerical values for various values of D, n, α and ℓ are obtained.

Approximate Solutions of D-Dimensional Klein-Gordon Equation with modified Hylleraas Potential

We study the D-dimensional Klein-Gordon equation for the modified Hylleraas potential with position dependent mass. We obtain the energy eigenvalues and the corresponding eigenfunctions for any arbitrary l-state using the parametric Nikiforov-Uvarov method. New elegant approximation method is used to deal with the centrifugal term. We also discuss the two limiting cases of this potential, i.e. the Woods-Saxon and Rosen-Morse potentials.

Exact Solutions of D-Dimensional Klein–Gordon Equation with an Energy-Dependent Potential by Using of Nikiforov–Uvarov Method

We study the D-dimensional Klein–Gordon equation for a particle in a hyperspherically-symmetric potential. The potentials we consider here depend linearly on energy and inversely on the hyperradius. We calculate the corresponding eigenfunctions and eigenvalues of this system by using the Nikiforov–Uvarov method. The results could find interesting applications in fields such as theoretical nuclear physics if one is considering a relativistic treatment of spin-zero systems.

Approximate Solution of D-Dimensional Klein—Gordon Equation with Hulthén-Type Potential via SUSYQM

Approximate analytical solutions of the D-dimensional Klein—Gordon equation are obtained for the scalar and vector general Hulthén-type potential and position-dependent mass with any l by using the concept of supersymmetric quantum mechanics (SUSYQM). The problem is numerically discussed for some cases of parameters.

Cornell and Coulomb interactions for the D‐dimensional Klein‐Gordon equation

AbstractWe investigate the D‐dimensional Klein‐Gordon equation in the presence of both Coulomb and Cornell potentials by quasi‐exact methodology. The Coulomb potential yields a degenerate result as the dimension increases, i.e. the quantum number l plays no role in the energy relation. For the Cornell potential, however, the behavior is different and no degeneracy exists. Closed form of eigenfunctions is reported and the energy behavior for different states is numerically discussed.

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

Abstract We 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.