A New Analytical Approach to Study the ‎Anharmonic and Morse Potentials of ‎Diatomic Molecules

Document Type : Research Paper

Authors

1 Department of Physics, Faculty of Sciences Dhar El Mehraz, University Sidi Mohamed Ben ‎Abdellah, P.O.Box 1796 Fes-Atlas, 30000, Fes, Morocco

2 Department of Physics, Faculty of Sciences Dhar El Mehraz, University Sidi Mohamed Ben ‎Abdellah, P.O.Box 5541 Fes-Sidi Brahim, 30000 Fes, Morocco

Abstract

   An appropriate analytical method has been used to solve the Schrödinger equation, for a polynomial anharmonic potential to obtain the eigen-energy levels, up to the second order. Moreover, the derived expression has been exploited in the case of the Morse potential that led to express the vibrational energy of diatomic molecules. The application of the proposed analytical method to some selected molecules makes it possible to obtain results that are in good agreement with those available in the literature, and proves that our approach can be a valuable aid in spectroscopic experiments.

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References

  1. Flügge, S., “Practical Quantum Mechanics”, Springer-Verlag, New York, (1994) 68-84.
  2. Wang, G., Guo, Q., Wu, L., Yang, X., “Giant Second-Order Optical Non-linearities in Anharmonic-Oscillator Potential Wells: Perturbation Theory Calculations”, Physica E, 39 (2007) 75-84.
  3. Fernandez, F. M., “Perturbation Theory with Canonical Transformations”, Rev., 45 (1992) 1333-1338.
  4. Popescu, V., “Combination of the variational and finite element methods for the D-dimensional generalized anharmonic oscillator”, Lett. A, 297 (2002) 338-343.
  5. Ciftci, H. L., Hall, R., Saad, N., “Asymptotic iteration method for eigenvalue problems”, Phys. A: Math. Gen., 36 (2003) 11807 –11816.
  6. Morse, P. M., “Diatomic Molecules According to the Wave Mechanics”, Rev., 34 (1929) 57-64.
  7. Pöschl, G., Teller, E., “Bemerkungen zur Quantenmechanik des anharmonischen Oszillators”, Zeitschrift für Physik, 83 (1933) 143-151.
  8. Varshni, Y. P., “Comparative Study of Potential Energy Functions for Diatomic Molecule”, Reviews of Modern Physics, 29 (1957) 664-682.
  9. Hamzavi, M., Ikhdair, S. M., Thylwe, E., “Equivalence of the empirical shifted Deng–Fan oscillator potential for diatomic molecules”, J. Math. Chem., 51 (2013) 227–238.
  10. Falaye, B. J., Ikhdair, S. M., Hamzavi, M., “The Energy States of Some Diatomic Molecules: The Exact Quantisation Rule Approach”, Naturforschung, 70 (2015) 85–90.
  11. Janati Idrissi, M., Fedoul, A., Sayouri, S., Amila, I., “Anharmonic Potentials Analysis through the Floquet Representation”, Journal of Applied Mathematics and Physics, 8 (2020) 184-195.
  12. Janati Idrissi, M., Fedoul, A., Sayouri, S., “Systematic Approach to Compute the Vibrational Energy Levels of Diatomic Molecules”, Journal of Applied Mathematics and Physics, 8 (2020) 2463-2474.
  13. Janati Idrissi, M., Fedoul, A., Achkar, Y., Chatwiti, A., Sayouri, S., “Squeezing in Floquet States and Quasi-Energies of Harmonic Oscillator Driven by a Strong Periodic Field”, African Journal of Mathematical Physics, 10 (2011) 21-30.
  14. Janati Idrissi, M., Fedoul, A., Sayouri, S., “Non-Perturbative Treatment of Quantum Mathieu Oscillator”, Journal of Applied Mathematics and Physics, 8 (2020) 698-709.
  15. Lochak, G., Thioun, M., “Sur une méthode générale de perturbation en mécanique ondulatoire et son utilisation dans les problèmes de resonance”. Journal of Physics, 30 (1969) 482-496.
  16. Clark Alexander, “A Closed Form Solution for Quantum Oscillator Perturbations Using Lie Algebras”, Journal of Physical Mathematics, 3 (2011) 1-12.
  17. Ikhdair, S. M., “Effective Schrodinger equation with general ordering ambiguity position-dependent mass Morse potential”, Molecular Physics, 110 (2012) 1415-1428.
  18. Nasser, I., Abdelmonem, M. S., Bahlouli, M. S., Alhaidari, A. D., “The Rotating Morse Potential Model for Diatomic Molecules in the Tridiagonal J-Matrix Representation: I. Bound States”, Journal of Physics B: Atomic, Molecular and Optical Physics, 40 (2007) 4245-4257.
  19. Kunc, J.A., Gordillo-Vázquez, F.J., “Rotational-Vibrational Levels of Diatomic Molecules Represented by the Tietz-HuaRotating Oscillator”, Phys. Chem. A, 101 (1997) 1595-1602.
  20. Vu, H., Atwood, M. R., Vodar, B., “1-0, 2-0, 3-0, Absorption Bands of Dense Forms of Pure CO and Its Solutions in N 2 and Ar”, The Journal of Chemical Physics, 38(11) (1963) 2671-2677.
  21. Irikura, K. K., “Experimental Vibrational Zero-Point Energies: Diatomic Molecules”, Phys. Chem. Ref. Data, 36(2) (2007) 389-397.
International Journal of Nanoscience and Nanotechnology
Volume 19, Issue 3
August 2023
Pages 165-172

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