Accidental Degeneracies in N dimensions for Potential Class αr 2d−2−βr d−2 via Asymptotic Iteration Method (AIM). (April 2017)

• Record Type: Journal Article
• Authors: Kisoglu, H. F.; Ciftci, Hakan
• Is Part Of: Communications in theoretical physics. Volume 67:Number 4(2017:Apr.)
• Publication Date: 2017-04
• Subjects: asymptotic iteration method -- perturbation method -- approximate solutions; 02.30.Hq -- 02.60.Cb -- 03.65.Ge -- 03.65.-w; Physics -- Periodicals; 530.105
• DOI: 10.1088/0253-6102/67/4/350
• Languages: English
• ISSNs: 0253-6102

Abstract

Abstract: 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 α r 2 d − 2 − β 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.