Exact bound state solutions of the s-wave Klein–Gordon equation with the generalized Hulthén potential

We present a new approximation scheme for the centrifugal term to solve the Schrodinger equation with the Hulthen potential for any arbitrary l -state by means of a mathematical Nikiforov-Uvarov (NU) method. We obtain the bound-state energy eigenvalues and the normalized corresponding eigenfunctions expressed in terms of the Jacobi polynomials or hypergeometric functions for a particle exposed to this potential field. Our numerical results of the energy eigenvalues are found to be in high agreement with those results obtained by using the program based on a numerical integration procedure. The s -wave (l = 0analytic solution for the binding energies and eigenfunctions of a particle are also calculated. The physical meaning of the approximate analytical solution is discussed. The present approximation scheme is systematic and accurate.

An improved approximation scheme for the centrifugal term and the Hulthén potential

We study the effect of spatially dependent mass functions over the solution of the Klein-Gordon equation in the (3 + 1 -dimensions for spinless bosonic particles where the mixed scalar-vector Coulomb-like field potentials and masses are directly proportional and inversely proportional to the distance from the force center. The exact bound-state energy eigenvalues and the corresponding wave functions of the Klein-Gordon equation for mixed scalar-vector and pure scalar Coulomb-like field potentials are obtained by means of the Nikiforov-Uvarov (NU) method. The energy spectrum is discussed for different scalar-vector potential mixing cases and also for the constant-mass case.

Exact Klein-Gordon equation with spatially dependent masses for unequal scalar-vector Coulomb-like potentials

Exact solutions of the Dirac equation with scalar and vector Hartmann potentials

We present a new approximation scheme for the centrifugal term to obtain a quasi-exact analytical bound state solution within the framework of the position-dependent effective mass radial Klein?Gordon equation with the scalar and vector Hulth?n potentials in any arbitrary D dimension and orbital angular momentum quantum numbers l. The Nikiforov?Uvarov (NU) method is used in the calculations. The relativistic real energy levels and corresponding eigenfunctions for the bound states with different screening parameters have been given in a closed form. It is found that the solutions in the case of constant mass and in the case of s-wave (l=0) are identical with the ones obtained in the literature.

Any l-state improved quasi-exact analytical solutions of the spatially dependent mass Klein–Gordon equation for the scalar and vector Hulthén potentials

A. Yunus

Papers

Continuum states of the Klein-Gordon equation for vector and scalar interactions