2008/10/09 by SAMEER M. IKHDAIR, Sameer M. Ikhdair · 27 citations
Mathematics · Physics and Astronomy · #Bound state #Eigenfunction #Eigenvalues and eigenvectors #Mathematical functions and polynomials #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #Scalar (mathematics) #Scalar potential #Vector Laplacian #Vector potential #quant-ph
paper · pdf · doi:10.1142/s0129183109013431
published in International Journal of Modern Physics C 20(01), 25-45 (World Scientific) · 25 pages
arxiv created 2008/10/09 · openalex publication_date 2009/01/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We solve the Klein–Gordon equation in any D-dimension for the scalar and vector general Hulthén-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 ≠ 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.