Abstract
Approximate analytical solutions of a two-term potential are studied for the relativistic wave equations, namely, for the Klein-Gordon and Dirac equations. The results are obtained by solving of a Riemann-type equation whose solution can be written in terms of hypergeometric function 2Fl(a,b; c; z). The energy eigenvalue equations and the corresponding normalized wave functions are given both for two wave equations. The results for some special cases including the Manning-Rosen potential, the Hulthen potential and the Coulomb potential are also discussed by setting the parameters as required.
Highlights
The investigation of the non-relativistic and relativistic bound/scattering state solutions of exponential-type potentials has become an important area within quantum mechanics
We tend to give the approximate, analytical solutions of the Klein-Gordon and Dirac equations which will be written in the form of a Riemann-type equation
We present briefly the results for the Manning-Rosen potential, the Hulthen potential and Coulomb potential by setting the potential parameters as required
Summary
The investigation of the non-relativistic and relativistic bound/scattering state solutions of exponential-type potentials has become an important area within quantum mechanics. Many authors have made much efforts to obtain the analytical solutions of the exponential-type potentials, especially about the problems based on the Morse potential, Hulthen potential, and the Woods-Saxon potential, with the help of various methods [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32]. Published under licence by IOP Publishing Ltd doi:10.1088/1742-6596/766/1/012002
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