On Solutions of the Killingbeck Potential and Clarifying Comments on a Related Analytical Approach

Abstract:The work presents analytical solutions to the Schrodinger equation for the Killingbeck potential, a Hybrid model combining harmonic, linear and Coulomb terms, and which is also an approximate model of Yukawa-type potentials. The radial Schrodinger equation is solved by means of the series expansion method, thus yielding the exact expressions of both bound-states solutions and eigen-functions for the systems; these systems include quarkonium and confined hydrogen-like atoms in plasma environments. Furthermore, we offer a constructive commentary on the work of Obu et al. (East Eur. J. Phys. 3, 146-157, 2023), with the aim of clarifying a mathematical misstatement used in their analytical treatment of analogous systems.

J.2; G.1.2; G.1.7; F.2.1

arXiv:2607.19611 [quant-ph]

(or arXiv:2607.19611v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.19611 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

https://doi.org/10.26565/2312-4334-2025-4-14 Focus to learn more DOI(s) linking to related resources

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