Revisiting the energy spectrum of the radial screened Coulomb potential

• Published in: Physica scripta 2024-06, Vol.99 (6), p.65404
• Main Authors: Xu, Lei, Fernández, Francisco M, Jiao, Li Guang, Montgomery, Henry E, Ho, Yew Kam, Fritzsche, Stephan
• Format: Article
• Language: English
• Subjects: asymptotic laws; energy spectrum; number of bound states; radial screened Coulomb potential
• ISSN: 0031-8949; 1402-4896
• DOI: 10.1088/1402-4896/ad42e5

We revisit the energy spectrum of the radial screened Coulomb potential V ( r ) = − exp ( − C / r ) / r and analyze the small- and large-parameter ( C ) asymptotic laws of the system eigenenergies in both the original and C -scaled Schrödinger equations. The discrepancy observed in our previous work [Xu et al (2023) Phys. Lett. A 483 , 129 064] with the numerical calculations of Stachura and Hancock [(2021) J. Phys. Commun. 5 , 065 004] is resolved by reinterpreting their results as the eigenenergies of two-body systems of equal mass. We derive an improved analytical expression for system energies at small values of C and an approximate asymptotic law for arbitrary l -state energies when C approaches infinity. The behavior of the scaled system energies and wave functions is analyzed in the large-parameter limit. The present study provides solid proof that the radial screened Coulomb potential supports an infinite number of bound states for finite values of screening parameter, which completes the investigation of the energy spectrum of this special potential.