Accidental Degeneracies in N dimensions for Potential Class αr ^2d−2−βr ^d−2 via Asymptotic Iteration Method (AIM)

In mathematical physics the main goal of quantum mechanics is to obtain the energy spectrum of an atomic system. In many practices, Schrödinger equation which is a second order and linear differential equation is solved to do this analysis. There are many theoretic mathematical methods serving this purpose. We use Asymptotic Iteration Method (AIM) to obtain the energy eigenvalues of Schrödinger equation in N-dimensional euclidean space for a potential class given as $\alpha r^{2d-2}-\beta r^{d-2}$. We also obtain a restriction on the eigenvalues that gives degeneracies. Besides, we crosscheck the eigenvalues and degeneracies using the perturbation theory in the view of the AIM. (paper)