An Analytical Expression for The Eigenvalues of The Potential Family 𝑽�(𝒓�)=𝑨� 𝒓� 𝟐� −𝑩� 𝒓� +𝑪�𝒓�𝜿�

Abstract

In the current study, we introduce an analytical form of the solution for the potential family 𝑽�(𝒓�)=𝑨� 𝒓� 𝟐� −𝑩� 𝒓� +𝑪�𝒓�𝜿�. The method which combines the perturbation theory (PT) and supersymmetric (SUSY) quantum theory results in an abstract equation of the energy eigenvalues (which can be named as closed analytical form method (CAFM)). The results of the asymptotic iteration method (AIM) and CAFM will be compared with the numerical method (NM) to test the validity of our approximation at the end of the work.