Treatment of a three-dimensional central potential with cubic singularity
Department of Physics and Physical Oceanography, Memorial University of Newfoundland, A1B3X7, Saint John’s, NL, Canada
2 Faculty of Technology and Applied Sciences, Al-Quds Open University, Nablus, Palestine
3 Physics Department, King Fahd University of Petroleum & Minerals, 31261, Dhahran, Saudi Arabia
Accepted: 19 December 2020
Published online: 6 January 2021
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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021