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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

Exact Classical and Quantum Mechanics of a Generalized Singular Equation of Quadratic Liénard Type

Lucas H. Koudahoun1, Jean Akande1, Damien K.K. Adjaï1, Yélomè J.F. Kpomahou2 and Marc D. Monsia1
  • 1 University of Abomey-Calavi, Benin
  • 2 University of Abomey, Benin

Abstract

Authors introduce a generalized singular differential equation of quadratic Liénard type for study of exact classical and quantum mechanical solutions. The equation is shown to exhibit periodic solutions and to include the linear harmonic oscillator equation and the Painlevé-Gambier XVII equation as special cases. It is also shown that the equation may exhibit discrete eigenstates as quantum behavior under Nikiforov-Uvarov approach after several point transformations.

Journal of Mathematics and Statistics
Volume 14 No. 1, 2018, 183-192

DOI: https://doi.org/10.3844/jmssp.2018.183.192

Submitted On: 21 March 2018 Published On: 5 July 2018

How to Cite: Koudahoun, L. H., Akande, J., Adjaï, D. K., Kpomahou, Y. J. & Monsia, M. D. (2018). Exact Classical and Quantum Mechanics of a Generalized Singular Equation of Quadratic Liénard Type. Journal of Mathematics and Statistics, 14(1), 183-192. https://doi.org/10.3844/jmssp.2018.183.192

Open AccessCopyright: © 2018 Lucas H. Koudahoun, Jean Akande, Damien K.K. Adjaï, Yélomè J.F. Kpomahou and Marc D. Monsia. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Painlevé-Gambier XVII Equation
  • Liénard Equation
  • Quantum Mechanics
  • Point Transformation
  • Nikiforov-Uvarov Method