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

Abstract

We present the exact and iterative solutions of the radial Schrödinger equation for a class of potentials, , for various values of κ 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 κ = 0, − 1 and −2. Nevertheless, there are no analytical solutions for the cases κ = 1 and 2. Therefore, the energy eigenvalues are obtained numerically. Our results are in excellent agreement with previous work.