Treatment of a three-dimensional central potential with cubic singularity

We compute the bound states for a special type of singular central potential that generalizes the hyperbolic Eckart potential by adding a cubic singular term at the origin while keeping the short range exponential decay far away from the origin. Such strong singular potentials are of practical importance in atomic, nuclear and molecular physics. To bring the solution of the Schrodinger equation for finite angular momentum to analytical treatment we use an analytical approximation to the centrifugal orbital part of the potential that has a similar structure to the Eckart potential. We compute the energy spectrum associated with this potential using both the tridiagonal representation approach (TRA) and the asymptotic iteration method (AIM) and make a comparative analysis of these results.