Abstract
Using some basic inequalities, the spherical Hellmann potential is assigned its place in the hierarchy of relative ordering, within the set of standard screened Coulomb potentials at all radial distances. The previously known comparison theorem applicable to the screened Coulomb potentials is thereby expanded to ascertain the relative ordering of energy levels for nℓ-states of Hellmann potential vis-a-vis those corresponding to the screened Coulomb potentials. The analytic results are supported by numerical calculation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hellmann H (1935) A new approximation method in the problem of many electrons. J Chem Phys 3:61–61
Yukawa H (1935) On the interaction of elementary particles. I. Proc Phys Math Soc Jpn 17:48–57
Hulthén L (1942) Über die Eigenlosungen der Schrödinger-gleichung des deuterons 28 A: 1–12
Roy AK (2016) Critical parameters and spherical confinement of H atom in screened coulomb potential. Intl J Quant Chem 116:953–960 (See refs 2–17 for numerical works)
Reed M, Simon B (1978) Methods of modern mathematical physics IV: analysis of operators. Academic, New York
Thirring W (1981) A course in mathematical physics 3: quantum mechanics of atoms and molecules. Springer, New York
Hall RH (1985) Envelope representations for screened Coulomb potentials. Phys Rev A 32:14–18
Wang XR (1992) General theorem on the Schrödinger equation. Phys Rev A 46:7295–7296
Stubbins C (1993) Bound states of the Hulthén and Yukawa potentials. Phys Rev A 48:220–227
Baye D, Sen KD (2008) Confined hydrogen atom by the Lagrange-mesh method: energies, mean radii, and dynamic polarizabilities. Phys Rev E 78:026701-(1–7)
Montgomery Jr HE, Sen KD, Katriel J (2018) Critical screening in the one- and two-electron Yukawa atoms. Phys Rev A 97:022503-(1–8)
Shukla PK, Eliasson BB (2008) Screening and wake potentials of a test charge in quantum plasmas. Phys Lett A 372:2897–2899
Acknowledgments
KDS thanks Indian National Science Academy for awarding a senior scientist position. He is grateful to Richard Hall for several useful comments and guidance. With great pleasure we record our appreciation of Pratim Chattaraj’s scientific contributions, which we wish to enthusiastically celebrate together with everyone.
Author information
Authors and Affiliations
Corresponding author
Additional information
This paper belongs to Topical Collection International Conference on Systems and Processes in Physics, Chemistry and Biology (ICSPPCB-2018) in honor of Professor Pratim K. Chattaraj on his sixtieth birthday
Rights and permissions
About this article
Cite this article
Sen, K.D., Mandal, D. A new comparison theorem on Hellmann potential. J Mol Model 24, 299 (2018). https://doi.org/10.1007/s00894-018-3840-3
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00894-018-3840-3