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 impor...

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Bibliographic Details
Published in:European physical journal plus 2021-01, Vol.136 (1), p.47, Article 47
Main Authors: Assi, I. A., Sous, A. J., Bahlouli, H.
Format: Article
Language:English
Subjects:
Angular momentum
Applied and Technical Physics
Approximation
Asymptotic methods
Atomic
Complex Systems
Condensed Matter Physics
Energy
Energy spectra
Iterative methods
Mathematical and Computational Physics
Molecular
Molecular physics
Nonlinear equations
Optical and Plasma Physics
Ordinary differential equations
Physics
Physics and Astronomy
Quantum physics
Regular Article
Schrodinger equation
Theoretical
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Summary: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.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/s13360-020-01032-0