Algebraic solution methods of diatomic and triatomic linear molecules

The energy eigenvalues and corresponding eigenfunctions of radial Schrödinger equation that has a few applications in literature are obtained by using the asymptotic iteration method (AIM) for diatomic and linear triatomic molecules. A novel approach to the analytical solution of Schrödinger equation for diatomic molecular potentials with any angular momentum is proposed within the framework of AIM. By using the proposed method, the spectrum of r^(-1)and r^(-2)type potentials of diatomic molecules in radial Schrödinger equation are calculated for some physical potentials such as Mie potential, Kratzer-Fues potential, Coulomb potential, and Pseudoharmonic potential by determining the alpha, beta, gamma and sigma parameters. This method supplies a high accuracy besides the simplicity in calculation of the corresponding spectrum of potentials.