Relativistic Approximate Solutions for a Two-Term Potential: Riemann-Type Equation

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 ${}_2{F}_1(a,b;c;z)$. 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 Hulthén potential and the Coulomb potential are also discussed by setting the parameters as required.

arXiv comment6 pages

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