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| This paper analyzes Klein-Gordon bound states with the direct coupling of Coumlombic vector and scalar singular potentials, viz V(r)=-(hcα)/r and S(r)=-(hcα’)/r with the order α’<α on R,where nonvanishing centrifugal effect is taken into account. To obtain the eigenfunction and energy spectrum, two approaches are put forward, the difference between which origins from the manipulations of the coefficient of the centrifugal term. In the first approach, the induced energy spectrum depends on the complete set of quantum numbers {n,l,m} explicitly; in the second approach this dependence is implicit, but it provides a simpler description of the asymptotic behaviors of the wave function at the infinity for compensation. Except for these differences, those two approaches share the same formulation and are in pleasant correspondence. Variable transformations lead the dynamical equation to a confluent hypergeometric equation, subsequently boundary conditions and normalization requirement abandon Kummer’s function of the second kind as a component of the eigenfunction, and break Kumemer’s function of the first kind off to a polynomial to act as the eigenfunction, which also yields the energy spectrum, analytically and explicitly. Eventually, calculation shows that the degree of degeneracy of the energy levels is n^2, and a brief numerical analysis is performed to explore whether extra constraints on {α,α’} would arise or not to guarantee the existence of bound states. |
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| Keywords:Klein-Gordon Equation;Centrifugal Effect;Coulombic Potential;Confluent Hypergeometric Equation;Degree of Degeneracy |
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