The Energy Spectra of Soluble Potentials Within the Framework of the Variational Method

Authors

  • Ekwevugbe Omugbe
    Obafemi Awolowo University Ile-Ife
  • Etido P. Inyang
  • Clement A. Onate

Keywords:

variational method, Coulomb potential, Pseudoharmonic potential, Hulthen potential, Poschl-Teller-type potential

Abstract

In this article, we demonstrated the use of the variational approach in solving the bound state solutions of the Schrödinger equation for solvable potential functions. The method has been applied to determine the exact analytical excited states energy spectra for the Coulomb, and Pseudo-harmonic potentials. Also, the exact analytical ground state energy spectra for the Hulthén and Pöschl-Teller-type potentials have been obtained in closed form. In addition, we obtained the approximate energy eigenvalues of an exponential potential which does not admit exact analytical closed form solution. By minimizing the total variational energy, the variational parameters were derived. The results for these potential functions align perfectly with those obtained through other methods in the existing literature and numerical solution with the Matrix Numerov approach. The results demonstrate that the accuracy of the variational approach is strongly correlated with the use of accurate trial wave functions. 

Dimensions

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Published

2026-07-03

How to Cite

Omugbe, E., Inyang, E. P., & Onate, C. A. (2026). The Energy Spectra of Soluble Potentials Within the Framework of the Variational Method. Nigerian Journal of Physics, 35(4), 17-25. https://doi.org/10.62292/njp.v34i2.2025.569

Issue

Vol. 35 No. 4 (2026): Nigerian Journal of Physics - Vol. 35 No. 4

Section

Articles
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Copyright (c) 2026 Ekwevugbe Omugbe, Etido P. Inyang, Clement A. Onate

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Omugbe, E., Inyang, E. P., & Onate, C. A. (2026). The Energy Spectra of Soluble Potentials Within the Framework of the Variational Method. Nigerian Journal of Physics, 35(4), 17-25. https://doi.org/10.62292/njp.v34i2.2025.569