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

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

2008-10-09

arxiv.org/abs/0810.1590v1

Physics

Quantum Physics

25 pages

Scientific paper

10.1142/S0129183109013431

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.

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