Bound state solutions and thermal properties of the N-dimensional Schrödinger equation with Varshni plus Woods-Saxon potential via Nikiforov-Uvarov method

Ridha Horchani, Safa Al-Shafii, Noora Al-Hashimi, Akpan N. Ikot, Ituen B. Okon, Uduakobong S. Okorie*, Carlos A. Duque, Enock O. Oladimeji

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We have solved the Schrödinger equation for Varshni plus Woods-Saxon potential in N-dimensions within the framework of Nikiforov-Uvarov method by using Greene-Aldrich approximation scheme to the centrifugal barrier term. We obtained the numerical bound state energies for both physical parameters and some diatomic molecules for various values of screening parameter which characterizes the strength of the potential. We obtained the energy eigen equation in a closed and compact form and applied it to study partition function and other thermodynamic properties as applied to four selected diatomic molecules namely: Nitrogen (N2), Carbon (II) Oxide (CO), Nitrogen Oxide (NO) and Hydrogen (H2) molecules, respectively using experimentally determined spectroscopic parameter. The numerical energy eigenvalues obtained both for physical parameters and for selected diatomic molecules at various dimensions (N= 2, 4 and 6) reveals that constant degeneracies occurs for S and P quantum state. The result also shows that 1S-quantum state has the highest bound state energies which are experimentally verified because of its proximity to the nucleus of an atom. To ascertain the accuracy of our work, the thermodynamic spectral diagram produces an excellent curves as compared to work of an existence literature. This research has application in the field of molecular spectroscopy.

Original languageEnglish
Article number162243
JournalJournal of Theoretical and Applied Physics
Issue number4
Publication statusPublished - Dec 2022
Externally publishedYes


  • Eigenvalues
  • N-dimensional Schrödinger equation
  • Nikiforov-Uvarov method
  • Varshni plus Woods-Saxon potential

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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