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Theoretic measure and thermal properties of a standard Morse potential model

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Abstract

Since the proposition of the standard form of Morse potential \(\left({V}_{SM}\left(r\right)\right)\) model over the years, there has not been much attention on the potential. Its application to different studies such as the thermodynamic properties and information theory are yet to be reported to the best of our understanding. In this study, the solutions of the radial Schrödinger equation for the standard Morse potential is obtained using supersymmetric approach. The effect of the quantum number on the energy eigenvalue for the standard Morse potential is examined numerically for the hydrogen molecule (H2), lithium molecule (Li2), and potassium molecule (K2). Using the energy equation and the wave function obtained, the theoretic measures and thermodynamic properties of hydrogen, lithium, and potassium molecules are calculated via maple program. It has been shown that the energy of the standard Morse potential is fully bounded for the three molecules studied. A higher concentration of electron density corresponds to a strongly localized distribution in the position configuration. The Beckner, Bialynicki-Birula, and Mycieslki (BBM) inequality is satisfied for both the ground state and the first excited state. Finally, the product of uncertainty obtained obeyed the Heisenberg uncertainty relation.

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Author information

Authors and Affiliations

  1. Department of Physics, Kogi State University, Anyigba, Nigeria

    C. A. Onate

  2. Department of Physics, University of Uyo, Uyo, Nigeria

    I. B. Okon & G. O. Jude

  3. Department of Physical Sciences, Redeemer’s University, P.M.B. 230, Ede, Nigeria

    U. E. Vincent

  4. Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK

    U. E. Vincent

  5. Department of Physics, University of Agriculture and Environmental Sciences, Umuagwo, Imo State, Nigeria

    E. Omugbe

  6. Department of Physics, School of Physical Sciences, Modibbo Adama University of Technology, Yola, Nigeria

    E. S. Eyube

  7. Theoretical Physics Group, Department of Physics, University of Port Harcourt, Choba, Nigeria

    M. C. Onyeaju

Authors
  1. C. A. Onate
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  2. I. B. Okon
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  3. U. E. Vincent
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  4. E. Omugbe
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  5. E. S. Eyube
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  6. M. C. Onyeaju
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  7. G. O. Jude
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Contributions

Formulation of the work: C.A. Onate. Calculations: C.A. Onate and E. Omugbe. Introduction: I.B. Okon and U.E. Vincent. Editing: M.C. Onyeaju. Numerical results/plotting: I.B. Okon and E.S. Eyube. Discussion of results: G.O. Jude.

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Correspondence to C. A. Onate.

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Onate, C.A., Okon, I.B., Vincent, U.E. et al. Theoretic measure and thermal properties of a standard Morse potential model. J Mol Model 29, 34 (2023). https://doi.org/10.1007/s00894-022-05441-z

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