Bound state solutions of the Schrödinger equation with energy-dependent molecular Kratzer potential via asymptotic iteration method

Akpan Ndem Ikot, Uduakobong Okorie, Alalibo Thompson Ngiagian, Clement Atachegbe Onate, Collins Okon Edet, Ita Okon Akpan, Precious Ogbonda Amadi


In this paper, we obtained the exact bound state energy spectrum of the Schrödinger equation with energy dependent molecular Kratzer potential using asymptotic iteration method (AIM). The corresponding wave function expressed in terms of the confluent hypergeometric function was also obtained. As a special case, when the energy slope parameter in the energy-dependent molecular Kratzer potential is set to zero, then the well-known molecular Kratzer potential is recovered. Numerical results for the energy eigenvlaues are also obtained for different quantum states, in the presence and absence of the energy slope parameter. These results are discussed extensively using graphical representation. Our results are seen to agree with the results in literature.

Full Text:



Chun-Feng, H., Zhong-Xiang, Z., Yan, L., Bound states of the Klein-Gordon equation with vector and scalar Wood-Saxon potentials, Acta Physica Sinica 8 (8) (1999) 561-565.

Sever, R., Tezan, C., Yesiltas, O., Bucurgat, M., Exact Solution of Effective Mass Schrödinger Equation for the Hulthen Potential, International Journal of Theoretical Physics 47 (9) (2008) 2243-2248.

Ikhdair, S. M., An approximate κ state solutions of the Dirac equation for the generalized Morse potential under spin and pseudospin symmetry, Journal of Mathematical Physics 52 (5) (2011) 1-22.

Maghsoodi, E., Hassanabadi, H., Zarrinkamar, S., Spectrum of Dirac Equation Under Deng–Fan Scalar and Vector Potentials and a Coulomb Tensor Interaction by SUSYQM, Few-Body Systems 53 (3-4) (2012) 525-538.

Ikot, A. N., Akpabio, L. E., Umoren, E. B., Exact Solution of Schrödinger Equation with Inverted Woods-Saxon and Manning-Rosen Potential, Journal of Scientific Research 3 (1) (2011) 25-33.

Qiang, W. C., Dong, S. H., Analytical approximations to the solutions of the Manning–Rosen potential with centrifugal term, Physics Letters A 368 (1-2) (2007) 13-17.

Yahya, W. A., Oyewumi, K. J., Thermodynamic properties and approximate solutions of the ℓ-state Pöschl–Teller-type potential, Journal of the Association of Arab Universities for Basic and Applied Sciences 21 (1) (2016) 53-58.

Sun, Y., He, S., Jia, C-S., Equivalence of the deformed modified Rosen–Morse potential energy model and the Tietz potential energy model, Physica Scripta 87 (2) (2013) 1-5.

Edet, C. O. and Okoi P. O., Any l-State Solutions of the Schrodinger Equation for q Deformed Hulthen plus Generalized Inverse Quadratic Yukawa Potential in Arbitrary Dimensions. Revista Mexicana de F´ısica 65 (2019) 333-344.

Edet, C. O., Okorie, U. S., Ngiangia, A. T., Ikot, A. N., Bound state solutions of the Schrodinger equation for the modified Kratzer potential plus screened Coulomb potential, Indian Journal of Physics (2019) 1-9.

Edet, C. O., Okoi P. O. and Chima S. O, Analytic solutions of the Schrödinger equation with non-central generalized inverse quadratic Yukawa potential. Revista Brasileira de Ensino de Física 42, e20190083, (2019) 1-9.

Ciftci, H., Hall, R. L., Saad, N., Asymptotic iteration method for eigenvalue problems, Journal of Physics A: Mathematical and General 36 (47) (2003) 11807-11816.

Falaye, B. J., Any ℓ-state solutions of the Eckart potential via asymptotic iteration method, Central European Journal of Physics 10 (4) (2012) 960-965.

Qiang, W. C., Dong, S. H., Proper quantization rule, EPL Europhysics Letters 89 (1) (2010) 10003.1-10003.2.

Ikhdair, S. M., Sever, R., Exact quantization rule to the Kratzer-type potentials: an application to the diatomic molecules, Journal of Mathematical Chemistry 45 (4) (2009) 1137-1152.

Okorie, U. S., Ikot, A. N., Edet, C. O.,Akpan, I.O., Sever R. and Rampho R., Solutions of the Klein Gordon equation with generalized hyperbolic potential in D-dimensions Journal of Physics Communication 3, 095015, (2019)

Onate, C. A., Ojonubah, J. O., Eigensolutions of the Schrödinger equation with a class of Yukawa potentials via supersymmetric approach, Journal of Theoretical and Applied Physics 10 (1) (2016) 21-26.

Ikot, A. N., Obong, H. P., Abbey, T. M., Zare, S., Ghafourian, M., Hassanabadi, H., Bound and scattering state of position dependent mass Klein–Gordon equation with Hulthen plus deformed-type hyperbolic potential, Few-Body Systems 57 (9) (2016) 807-822.

Onate, C. A., Onyeaju, M. C., Ikot, A. N., Ojonubah, J. O., Analytical solutions of the Klein–Gordon equation with a combined potential, Chinese Journal of Physics 54 (5) (2016) 820-829.

Onate, C. A., Ikot, A. N., Onyeaju, M. C., Udoh, M. E., Bound state solutions of D-dimensional Klein–Gordon equation with hyperbolic potential, Karbala International Journal of Modern Science 3 (1) (2017) 1-7.

Sadeghi, J., Factorization method and solution of the non-central modified Kratzer potential, Acta Physica Polonica A 112 (1) (2007) 23-28.

Kratzer, A., Die ultraroten rotationsspektren der halogenwasserstoffe, Zeitschrift für Physik A Hadrons and Nuclei 3 (5) (1920) 289-307.

LeRoy, R. J., Bernstein, R. B., Dissociation energy and long‐range potential of diatomic molecules from vibrational spacings of higher levels, The Journal of Chemical Physics 52 (8) (1970) 3869-3879.

Ikhdair, S. M., An approximate κ state solutions of the Dirac equation for the generalized Morse potential under spin and pseudospin symmetry, Journal of Mathematical Physics 52 (5) (2011) 052303.1-052303.22.

Saad, N., Hall, R. J., Cifti H., The Klein-Gordon equation with the Kratzer potential in d dimensions, Central European Journal of Physics 6 (3) (2008) 717-729.

Hassanabadi, H., Rahimov, H., Zarrinkamar, S. Approximate solutions of Klein-Gordon equation with Kratzer potential, Advances in High Energy Physics 2011 (2011) 1-7.

Budaca R., Bohr Hamiltonian with an energy-dependent γ-unstable Coulomb-like potential, The European Physical Journal A 52 (2016) 314.

Lombard, R. J., Mareš. J., The many-body problem with an energy-dependent confining potential, Physics Letters A 373 (4) (2009) 426-429.

Bayrak, O., Boztosun, I., Ciftci, H., Exact analytical solutions to the kratzer potential by the asymptotic iteration method, International Journal of Quantum Chemistry 107 (3) (2007) 540-544.

Hassanabadi, H., Zarrinkamar, S., Rajabi, A. A., Exact solutions of D-dimensional Schrödinger equation for an energy-dependent potential by NU method, Communications in Theoretical Physics 55 (4) (2011) 541-544.

Hassanabadi, H., Zarrinkamar, S., Hamzavi, H., Rajabi, A. A., Exact solutions of D-dimensional Klein–Gordon equation with an energy-dependent potential by using of Nikiforov–Uvarov method, Arabian Journal for Science and Engineering 37 (1) (2012) 209-215.

Boumali, A., Labidi, M., Shannon entropy and Fisher information of the one-dimensional Klein–Gordon oscillator with energy-dependent potential, Modern Physics Letters A 33 (6) (2018) 1-26.

Lombard, R. J., Mareš, J., Volpe, C., Wave equation with energy-dependent potentials for confined systems, Journal of Physics G: Nuclear and Particle Physics 34 (9) (2007) 1879-1889.

Gupta, P., Mehrotra, I., Study of heavy quarkonium with energy dependent Potential, Journal of Modern Physics 3 (10) (2012) 1530-1536.

Ikot, A. N., Chukwuocha, E. O., Onyeaju, M. C., Onate, C. A., Ita, B. I., Udoh, M. E., Thermodynamics properties of diatomic molecules with general molecular potential, Pramana 90 (2) (2018) 22-30.

Falaye, B. J., Corrigendum: Energy spectrum for trigonometric Pöschl–Teller potential solved by the asymptotic iteration method, Canadian Journal of Physics 91 (4) (2013) 365-367.



  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


Digital directories


Print version ISSN 0100-4670  On-line version ISSN 1678-4618 

Public Copyright License