An algebraic method for the analytical solutions of the Klein-Gordon equation for any angular momentum for some diatomic potentials

Akçay, Hüseyin
Sever, Ramazan
Analytical solutions of the Klein-Gordon equation are obtained by reducing the radial part of the wave equation to a standard form of a second-order differential equation. Differential equations of this standard form are solvable in terms of hypergeometric functions and we give an algebraic formulation for the bound state wave functions and for the energy eigenvalues. This formulation is applied for the solutions of the Klein-Gordon equation with some diatomic potentials.


The Dirac-Yukawa problem in view of pseudospin symmetry
AYDOĞDU, OKTAY; Sever, Ramazan (IOP Publishing, 2011-08-01)
An approximate analytical solution of the Dirac equation for the Yukawa potential under the pseudospin symmetry condition is obtained using the asymptotic iteration method. We discover the energy eigenvalue equation and some of the numerical results are listed. Wave functions are obtained in terms of hypergeometric functions. Extra degeneracies are removed by adding a new term, A/r(2), to the Yukawa potential. The effects of tensor interaction on the two states in the pseudospin doublet are also investigated.
Approximate analytical solutions of the Klein-Gordon equation for the Hulthen potential with the position-dependent mass
Arda, Altug; Sever, Ramazan; TEZCAN, CEVDET (IOP Publishing, 2009-01-01)
The Klein-Gordon equation is solved approximately for the Hulthen potential for any angular momentum quantum number l with the position-dependent mass. Solutions are obtained by reducing the Klein-Gordon equation into a Schrodinger-like differential equation using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get energy eigenvalues and the wavefunctions. It is found that the results in the case of constant mass are in good agreement with the ones obtain...
A Fourier-Bessel expansion for solving radial Schrodinger equation in two dimensions
Taşeli, Hasan (Wiley, 1997-02-15)
The spectrum of the two-dimensional Schrodinger equation for polynomial oscillators bounded by infinitely high potentials, where the eigenvalue problem is defined on a finite interval r is an element of [0, L), is variationally studied. The wave function is expanded into a Fourier-Bessel series, and matrix elements in terms of integrals involving Bessel functions are evaluated analytically. Numerical results presented accurate to 30 digits show that, by the time L approaches a critical value, the tow-lying ...
Solution of the Dirac equation for pseudoharmonic potential by using the Nikiforov-Uvarov method
Aydogdu, Oktay; Sever, Ramazan (IOP Publishing, 2009-07-01)
We investigate the energy spectra and corresponding wave functions of the Dirac equation for pseudoharmonic potential with spin and pseudospin symmetry. To obtain an analytical solution of the Dirac equation, we consider the Nikiforov-Uvarov method in the calculations. For any spin-orbit coupling term kappa, we find the closed forms of the energy eigenvalues and also obtain the radial wave functions in the spin and pseudospin symmetry limits.
BILIKMEN, S; NAZIH, RM (IOP Publishing, 1993-02-01)
In this paper, a nonlinear analytical solution for a cold plasma-bunched beam system based on the Hamiltonian formalism where alpha = n(b)/n0 and beta(phi) = upsilon(phi)/c have been taken as parameters matching between zero and unity is given. The oscillation limiting energies, frequencies and transformer ratios have been carried out in general for both the one-dimensional and the case where a small transverse component of motion is included. The plasma wakefield accelerator has been treated as a special c...
Citation Formats
H. Akçay and R. Sever, “An algebraic method for the analytical solutions of the Klein-Gordon equation for any angular momentum for some diatomic potentials,” PHYSICA SCRIPTA, pp. 0–0, 2014, Accessed: 00, 2020. [Online]. Available: