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We present the exact and iterative solutions of the radial Schr\"{o}dingerequation for a class of potential,$V(r)=\frac{A}{r^{2}}-\frac{B}{r}+Cr^{\kappa}$, for various values of $\kappa$from -2 to 2, for any $n$ and $l$ quantum states by applying the asymptoticiteration method. The global analysis of this potential family by using theasymptotic iteration method results in exact analytical solutions for thevalues of $\kappa=0 ,-1$ and -2. Nevertheless, there are no analyticalsolutions for the cases $\kappa=1$ and 2. Therefore, the energy eigenvalues areobtained numerically. Our results are in excellent agreement with the previousworks.Comment: 12 pages and 5 table

Solution of the radial Schrödinger equation for the potential family using the asymptotic iteration method