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

2025/12/08 by Fatma Zohra Khaled, Mustafa Moumni, Mokhtar Falek · 1 citation
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Dust and Plasma Wave Phenomena #Quantum and Classical Electrodynamics

paper · pdf · doi:10.26565/2312-4334-2025-4-14

Abstract

The work presents analytical solutions to the Schrödinger equation for the Killingbeck potential, a hybrid model combining harmonic, linear, and Coulombic terms, as well as an approximate model of Yukawa-type potentials. The radial Schrödinger equation is solved by means of the series expansion method, thus yielding the exact expressions of both bound-state solutions and eigen-functions for systems such as 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 utilised in their analytical treatment of analogous systems.

Cited by

• Bound states of the hydrogen-like atomic systems in plasma environments

Related

• Bound states of the hydrogen-like atomic systems in plasma environments
• Analytic Solution of Strongly Coupling Schroedinger Equations
• Bound state solutions of the Schrödinger equation for the atomic systems interacting with the radial screened Coulomb potential: analytical approximation methods
• Three Dimensional Confinement : WKB Revisited
• Missing solution in a relativistic Killingbeck potential