Solution of the Radial Schr\"{o}dinger Equation for the Potential Family $V(r)=\frac{A}{r^{2}}-\frac{B}{r}+Cr^{\kappa}$ using the Asymptotic Iteration Method

Abstract

We present the exact and iterative solutions of the radial Schr\"{o}dinger equation 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 asymptotic iteration method. The global analysis of this potential family by using the asymptotic iteration method results in exact analytical solutions for the values of $\kappa=0 ,-1$ and -2. Nevertheless, there are no analytical solutions for the cases $\kappa=1$ and 2. Therefore, the energy eigenvalues are obtained numerically. Our results are in excellent agreement with the previous works.