Involving Nikiforov-Uvarov Method in Schrodinger Equation Obtaining Hartmann Potential

  • Mahmoud A. Al-Hawamdeh Department of Physics, Mutah University, Jordan
  • Abdulrahman N. Akour Department of Basic Scientific Sciences, Al-Huson college, Al-Balqa Applied University, Jordan https://orcid.org/0000-0002-9026-4098
  • Emad K. Jaradat Department of Physics, Mutah University, Jordan
  • Omar K. Jaradat Department of Mathematic, Mutah University, Jordan
Keywords: Schrödinger equation, Nikiforov-Uvarov method, Hartmann Potential

Abstract

The total wave function and the bound state energy are investigated by involving the Nikiforov-Uvarov method to the Schrodinger equation in spherical coordinates employing Hartmann Potential (HP). The HP is considered as the non-central potential that is mostly recognized in nuclear field potentials. Every wave function is specified by a principal quantum number n, angular momentum number l, and magnetic quantum number m. The radial part of the wave function is obtained in terms of the associated Laguerre polynomial, using the coordinate transformation x=cosθ to obtain the angular wave function that depends on inverse associated Legendre polynomials.

Downloads

Download data is not yet available.

References

G.G. Blado, Theor. Chim. Acta, 94, 53 (1996). https://doi.org/10.1007/BF00190155

C. Chang-Yuan, L. U. Fa-Lin, and S. Dong-Sheng. Theor. Phys. 45, 889 (2006).

C. Quesne, J. Phys. A: Math. Gen. 21, 3093 (1988). https://doi.org/10.1088/0305-4470/21/14/010

C.Y. Chen, and S.H. Dong, Physics Letters, Section A: General, Atomic and Solid-State Physics, 335(5–6), 374 (2005). https://doi.org/10.1016/j.physleta.2004.12.062

D. Griffiths, and D.F. Schroeter, Introduction to quantum mechanics, 3rd ed, (United Kingdom, 2018), pp. 172-175.

S.P. Singh, European J. of Physics Education, 10(4), 1309 (2019). https://typeset.io/pdf/solving-hydrogen-atom-problem-using-spherical-polar-1ml17d8yfi.pdf

A.F. Nikiforov, and V.B. Uvarov. Special Functions of Mathematical physics, (Birkhäuser Verlag, Basel 1988), pp.1-20.

C. Berkdemir, Application of the Nikiforov-Uvarov Method in Quantum Mechanics: a Unified Introduction with Applications, edited by M.R. Pahlavani, (Pennsylvania State University, USA, 2012), https://doi.org/10.5772/33510

M. Abusini, M. Serhan, M.F. Al-Jamal, A. Al-Jamel, and E.M. Rabei, Pramana - Journal of Physics. 93, 93 (2019), https://doi.org/10.1007/s12043-019-1860-x

H. Mansour, and A. Gamal. Advance In High Energy Physics, 2018, 7269657 (2018). https://doi.org/10.1155/2018/7269657

M. Abu-Shady. International Journal of Modern Physics A, 34 (31), 1950201 (2019), https://doi.org/10.1142/S0217751X19502014

I.B. Okon, O. Popoola, and C.N. Isonguyo, Advances in High Energy Physics, 2017, Article 9671816 (2017), https://doi.org/10.1155/2017/9671816

M.R. Spiegel, S. Lipschutz, and J. Liu, Mathematical Handbook of Formulas and Tables, 3rd ed, (McGraw-Hill, 2008)

C.Y. Chen, F.L. Lu, D.S. Sun, Y. You, and S.H. Dong, Appl Math. Lett. 40, 90 (2015). https://doi.org/10.1016/j.aml.2014.10.001

A.D. Antia, C.C. Eze, and L.E. Akpabio, Physics & Astronomy International Journal, 2 (3), 187 (2018), https://doi.org/10.15406/paij.2018.02.00084

Published
2023-06-02
Cited
How to Cite
Al-Hawamdeh, M. A., Akour, A. N., Jaradat, E. K., & Jaradat, O. K. (2023). Involving Nikiforov-Uvarov Method in Schrodinger Equation Obtaining Hartmann Potential. East European Journal of Physics, (2), 117-123. https://doi.org/10.26565/2312-4334-2023-2-10