Approximate Solution of Schrodinger Equation to Diatomic Molecule for Harmonic Oscillator
DOI:
https://doi.org/10.56919/usci.2322.005Keywords:
Schrodinger equation, Diatomic molecule, Harmonic oscillator, Newton’s lawAbstract
This study has described the approximate solution of Schrodinger equation to diatomic molecule for harmonic oscillator. The solution procedure is developed by the Power series method and Newton’s second law. It consider an approximate solution of harmonic oscillator using Schrödinger equation in one dimension only because other analytical approaches are limited to the widely known method and consider two to five dimensions with various iteration method to obtain their results but here the solutions to be obtained and their efficiency will help other research to comprehend how the solution of this harmonic oscillator has been done over the years and also to use the most efficient approximate solution.
References
Akaninyeye D. A., Christian, C. E., Louis Z. A. (2019). Solution of the Schrodinger Equations with the Harmonic Oscillator potential (HOP) in Cylindrical Basis. Physics & Astronomy International Journal, 2(3), 187-191. DOI: https://doi.org/10.15406/paij.2018.02.00084
Alakesh, B., Lingraj, K., Bikash, K. B., Prasanta K. P. (2019). Experimental Demonstration of Force Driven Quantum Harmonic Oscillator in IBM Quantum Computer arXiv: 1906.01436V1.
Alharbey R. A., Gasim H., Al-Showaikh F. N. M., Hassan S. S. (2019). Chirped Gaussian Pulse Excitation of a Harmonic Oscillator. Physical Science International Journal,20(4),1-2. DOI: https://doi.org/10.9734/PSIJ/2018/46248
Bonilla M., Rosas-Ortiz O. (2017). The Harmonic Oscillator in the Framework of Scale DOI: https://doi.org/10.1088/1742-6596/839/1/012009
Relativity. Journal of Physics.
Chang J. (2019). Responses to Frequency Modulation in a Quantum Harmonic Oscillator. SCIREA Journal of Physics, 3(1), 1-9.
David W. W., Sabine M. V., (2006). How to Derive the Schrodinger Equation. Am.J.Phys./Ward, 1-12.
David J. G. (2004). Introduction to Quantum Mechanics (2nd ed.). Benjamin Cummings. ISBN 978-0-13-124405-4.
Harko T., Liang S. (2018). Exact solutions of the Lienard and generalized Lienard type ordinary non-linear differential equations obtained by deforming the phase space coordinates of the linear harmonic oscillator. arXiv:1505.02364v3 [math-ph].
Lambert N. (2001) Numerical Solutions of Schrödinger's Equation, TB2 :1-24.
Lawson L. M., Gabriel Y. H. A., Laure G. (2017). Lewis-Riesenfeld quantization and SU (1,1) coherent states for 2D damped harmonic oscillator. arXiv.1805.02484v1 [math-ph]. DOI: https://doi.org/10.1063/1.5045621
Richard H. (2018). Solutions of the fractional Schrodinger equation via diagonalization-A plea for the harmonic oscillator basis. arXiv:1805.03019v1 [physics.gen-ph]
Schrödinger, E. (1926)."An Undulatory Theory of the Mechanics of Atoms and Molecules". Phys.Rev. 28 (6):1049-070. Bibcode:1926PhRv...28.1049S. DOI: https://doi.org/10.1103/PhysRev.28.1049
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