Bound states of the Klein-Gordon equation for vector and scalar general Hulthen-type potentials in D-dimension

TL;DR

This paper analytically solves the Klein-Gordon equation with Hulthén-type potentials in arbitrary dimensions, deriving bound state energies and wavefunctions using the Nikiforov-Uvarov method, and compares results with existing studies.

Contribution

It provides a general analytical solution for the Klein-Gordon equation with Hulthén-type potentials in D-dimensions, including energy eigenvalues and eigenfunctions for various potential parameters.

Findings

Eigenvalues and eigenfunctions are obtained in closed form.

Results agree with previous studies in 1D and 3D cases.

Calculated binding energies for specific states and potentials.

Abstract

We solve the Klein-Gordon equation in any $D$-dimension for the scalar and vector general Hulth\'{e}n-type potentials with any $l$ by using an approximation scheme for the centrifugal potential. Nikiforov-Uvarov method is used in the calculations. We obtain the bound state energy eigenvalues and the corresponding eigenfunctions of spin-zero particles in terms of Jacobi polynomials. The eigenfunctions are physical and the energy eigenvalues are in good agreement with those results obtained by other methods for D=1 and 3 dimensions. Our results are valid for $q=1$ value when $l\neq 0$ and for any $q$ value when $l=0$ and D=1 or 3. The $s$% -wave ($l=0$) binding energies for a particle of rest mass $m_{0}=1$ are calculated for the three lower-lying states $(n=0,1,2)$ using pure vector and pure scalar potentials.