Approximate energy spectra of diatomic molecules (LiH, HCl, VH, I2) case of the Hulthén plus screened Kratzer potential
DOI:
https://doi.org/10.31349/RevMexFis.71.020402Keywords:
Schrodinger equation; spectra of energy; screened Kratzer potential, Hulthen potential, Nikiforov Uvarov functional analysis approach.Abstract
In this research, we used the Nikiforov Uvarov functional analysis method to solve the Schrödinger equation with the Hulthén plus screened Kratzer potential using the Greene Aldrich approximation to remove the centrifugal barrier. We determine the bound state energies and corresponding wave functions. We applied our results to several diatomic molecules (LiH, HCl, VH, and I2) to analyze their energy spectra. Our technique produced accurate results, which were validated by comparing our eigenvalue data with numerical data obtained by other researchers. Given the precision of this analytical method, we recommend its application in solving problems in non-relativistic and relativistic systems, particularly those involving exponential potentials.
References
L. Kantorovich, Quantum theory of the solid state: an introduction, Springer Science & Business Media (2004)
J. M. Blatt, and V. F. Weisskopf, Theoretical nuclear physics, Springer Science & Business Media (2012)
P. Strange, Relativistic Quantum Mechanics: with applications in condensed matter and atomic physics, Cambridge University Press (1998)
H. Haken, and H. C. Wolf, Molecular physics and elements of quantum chemistry: introduction to experiments and theory, Springer Science & Business Media (2013)
C. Berkdemir, Application of the Nikiforov-Uvarov method in quantum mechanics. Theoretical Concepts of Quantum Mechanics 225 (2012)
Jr. S. C. Miller and R. Good Jr, A WKB-type approximation to the Schrödinger equation. Physical Review 91 (1953) 174
C. Garrod, Hamiltonian path-integral methods. Reviews of modern Physics 38 (1966) 483
J. David, and C. Fernandez, Supersymmetric quantum mechanics. AIP Conference Proceedings, American Institute of Physics (2010)
N. H. Sweilam, and R. Al-Bar, Variational iteration method for coupled nonlinear Schrödinger equations. Computers & Mathematics with Applications 54 (2007) 993-999
K. Reggab, A. Gueddim and A. Naas, Semi-inverse variational approach to solve the Klein-Gordon equation for harmonic-and perturbed Coulomb potentials. Studies in Engineering and Exact Sciences 4 (2023) 248-267
F. A. Berezin, and M. Shubin, The Schrödinger Equation, Springer Science & Business Media (2012)
H. Kragh, Equation with the many fathers. The Klein-Gordon equation in 1926. American Journal of Physics 52 (1984) 1024- 1033
B. Thaller, The Dirac equation, Springer Science & Business Media (2013)
A. Kratzer, Die ultraroten rotationsspektren der halogenwasserstoffe. Zeitschrift für Physik 3 (1920) 289-307
J. Rowlinson, The Yukawa potential. Physica A: Statistical Mechanics and its Applications 156 (1989) 15-34
E. A. Hylleraas, Energy formula and potential distribution of diatomic molecules. The Journal of Chemical Physics 3 (1935) 595-595
A. D. S. Mesa, C. Quesne and Y. F. Smirnov, Generalized Morse potential: symmetry and satellite potentials. Journal of Physics A: Mathematical and General 31 (1998) 321
S. M. Ikhdair and R. Sever, Cent. Euro. J. Phys. 8 (2010) 652
M. Hamzavi, K.-E. Thylwe and A. Rajabi, Approximate bound states solution of the Hellmann potential. Communications in Theoretical Physics 60 (2013) 1
R. Greene and C. Aldrich, Variational wave functions for a screened Coulomb potential. Physical Review A 14 (1976) 2363
F. Rogers, H. Graboske Jr and D. Harwood, Bound eigenstates of the static screened Coulomb potential. Physical Review A 1 (1970) 1577
Ikot, A. et al., Eigensolution, expectation values and thermodynamic properties of the screened Kratzer potential. The European Physical Journal Plus 134 (2019) 386
D. Agboola, The Hulthen potential in D-dimensions. Physica Scripta 80 (2009) 065304
B. I. Ita et al., Bound state solutions of Schrödinger equation for a more general exponential screened coulomb potential via Nikiforov-Uvarov method. Ecletica Química 35 (2010) 103- 107
U. Okorie et al., Thermodynamic functions for diatomic molecules with modified Kratzer plus screened Coulomb potential. Indian Journal of Physics 95 (2021) 411-421
A. Ghanbari and S. M. Jadbaba, Thermal Functions of Diatomic Molecules Using Hulthen Plus Screened Kratzer Potential. Journal of Low Temperature Physics 211 (2023) 109-123
E. William et al., Ro-vibrational energies and expectation values of selected diatomic molecules via Varshni plus modified Kratzer potential model. Indian Journal of Physics 96 (2022) 3461-3476
E. Inyang et al., Solutions of the Schrödinger equation with Hulthen-screened Kratzer potential: application to diatomic molecules. East European Journal of Physics (2022) 12-22
C. N. Isonguyo et al., Eigensolutions and thermodynamic properties of Kratzer plus generalized Morse potential. Frontiers in Physics 10 (2022) 962717
J. Obu, P. Okoi and U. Okorie, Relativistic and nonrelativistic treatment of Hulthen-Kratzer potential model in D-dimensions. Indian Journal of Physics 95 (2021) 505-514
K. Reggab, Energy spectrum of selected diatomic molecules (H2, CO, I2, NO) by the resolution of Schrödinger equation for combined potentials via NUFA method. Journal of Molecular Modeling 30 (2024) 53
K. Reggab, Energy spectrum of some diatomic molecules using Nikiforov-Uvarov functional analysis. Physica Scripta 99 (2024) 025234
E. Omugbe, et al., Non-relativistic energy equations for diatomic molecules constrained in a deformed hyperbolic potential function. Journal of Molecular Modeling 30 (2024) 74
E. Omugbe, et al., Non-relativistic energy spectra of and diatomic molecules confined in a modified Scarf potential via supersymmetric WKB approach. Molecular Physics, (2024) e2390591
E. S. William, et al., Theoretic analysis of non-relativistic equation with the Varshni-Eckart potential model in cosmic string topological defects geometry and external fields for the selected diatomic molecules. Molecular Physics 122 (2024) e2249140
F. Ahmed, and S. K. Nayek Impact of topological defects and Yukawa potential combined with inverse square on eigenvalue spectra of diatomic molecules O 2, NO, LiH, HCl. Physica Scripta 99 (2024) 025401
L. K. Permatahati, et al., Relativistic energy spectra of diatomic molecules through the solutions of general conformable fractional (GCF) Klein-Gordon equation for Hulthen potential with position-dependent mass (PDM) and the thermodynamic properties. Molecular Physics, (2024) e2356182
C. N. Isonguyo, et al., Effects of magnetic and Aharonov-Bohm flux fields on information entropy with modified Kratzer plus screened Coulomb potential for selected diatomic molecules. Molecular Physics, (2024) e2338400
E. P. I., A. N. R. and A. SA Energy spectra, expectation values, and thermodynamic properties of HCl and LiH diatomic molecules. Eurasian Physical Technical Journal 21 (2024)
B. Dutta, S. K. Nayek and B. Pradhan Combined effect of ABflux field and inverse square plus Yukawa potential on diatomic molecules placed at point-like global monopole. The European Physical Journal Plus 139 (2024) 125
A. Ikot, et al., The Nikiforov-Uvarov-Functional Analysis (NUFA) Method: A new approach for solving exponential-type potentials. Few-Body Systems 62 (2021) 1-16
A. A. Khelashvili and T. P. Nadareishvili What is the boundary condition for the radial wave function of the Schrödinger ¨ equation? American Journal of Physics 79 (2011) 668-671
R. Greene, and C. Aldrich Variational wave functions for a screened Coulomb potential. Physical Review A 14 (1976) 2363
O. Oluwadare, and K. Oyewumi Energy spectra and the expectation values of diatomic molecules confined by the shifted Deng-Fan potential. The European Physical Journal Plus 133 (2018) 422
C. Edet, and A. Ikot Analysis of the impact of external fields on the energy spectra and thermo-magnetic properties of N2, I2, CO, NO and HCl diatomic molecules. Molecular Physics 119 (2021) e1957170
I. Okon, et al., Aharonov-Bohm (AB) flux and thermomagnetic properties of Hellmann plus screened Kratzer potential as applied to diatomic molecules using Nikiforov-UvarovFunctional-Analysis (NUFA) method. Molecular Physics 120 (2022) e2046295
N. Akpan Ikot, S. Uduakobong Okorie, J. Ramazan Sever, G. J. Rampho, Eigen solution expectation values and thermodynamic properties of the screened Kratzer potential, The European Physical Journal Plus, 134 (2019) (386)
E. Omugbe et al., Any l l-State Energy of the Spinless Salpeter Equation Under the Cornell Potential by the WKB Approximation Method: An Application to Mass Spectra of Mesons. Few-Body Systems 63 (2022) 1-7
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Khaled Reggab

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.