Solutions to Molecular Vibration Potentials in D-dimensions using the Asymptotic Iteration Method.

Abstract

We study the bound-state solutions of some molecular vibration potentials-harmonic oscillator, pseudoharmonic oscillator and the Kratzer-Fues - by solving the D-dimensional Schrödinger equation using the Asymptotic Iteration Method (AIM). The eigenvalues and the corresponding eigenfunctions are also obtained using the AIM. It was found that the asymptotic iteration method gives the eigenvalues directly by some transformation of the radial Schrödinger equation; likewise, the asymptotic iteration method yields exact analytical solutions for exactly solvable problems and provides the closed-forms for the energy eigenvalues as well as the corresponding eigenfunctions.

Keywords: Schrödinger Equation, Asymptotic Iterative method, Mie-type potentials, Bound State.