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BOUND STATES OF THE KLEIN–GORDON EQUATION FOR VECTOR AND SCALAR GENERAL HULTHÉN-TYPE POTENTIALS IN D-DIMENSION

Sameer M. Ikhdair

Open publisher page 24 citations

Abstract

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 m0 = 1 are calculated for the three lower-lying states (n = 0, 1, 2) using pure vector and pure scalar potentials.

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What this paper is about

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 m0 = 1 are calculated for the three lower-lying states (n = 0, 1, 2) using pure vector and pure scalar potentials.

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Available abstract

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 m0 = 1 are calculated for the three lower-lying states (n = 0, 1, 2) using pure vector and pure scalar potentials.

Key concepts: Eigenfunction, Eigenvalues and eigenvectors, Scalar (mathematics), Bound state, Mathematical physics, Dimension (graph theory), Physics, Klein–Gordon equation

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BOUND STATES OF THE KLEIN–GORDON EQUATION FOR VECTOR AND SCALAR GENERAL HULTHÉN-TYPE POTENTIALS IN D-DIMENSION — Research Paper | ScholarLens