On the q-deformed exponential-type potentials

  • G. OvandoEmail author
  • J. J. Peña
  • J. Morales
  • J. García-Ravelo
  • J. García-Martínez
Regular Article
Part of the following topical collections:
  1. CHITEL 2017 - Paris - France


In this work, both non-deformed and q-deformed exactly solvable multiparameter exponential-type potentials \(V^{\pm }(r)\) are obtained; \(V^{+}(r=x)\) stands for one-dimensional potential and \(V^{-}(r)\) for the radial part of s-states used in the treatment of vibrational properties of diatomic molecules. As a first result, we show that non-deformed potentials arise from non-q-dependent parameters involved in \(V^{\pm }(r)\) and rather correspond to a class of q-shifted exponential-type potentials obtained from the Arai’s q-deformed hyperbolic functions. As a second result, by using q-dependent parameters in \(V^{\pm }(r)\) it is possible to obtain true q-deformed exponential-type potentials. As a useful application of these potentials, some examples of q-deformed exponential-type potentials are considered by means of a proper selection of the involved parameters. Our proposal is general and can be viewed as a unified treatment to the study of q-deformed exponential-type potentials with the advantage that it is not necessary to use a specialized method for solving the Schrödinger equation to each specific potential because many of them are obtained as particular cases of \(V^{\pm }(r)\). Furthermore, new q-deformed potentials used as interesting alternatives in quantum chemical applications can be derived.


Canonical transformation Schrödinger-like equation Hypergeometric DE q-deformed exponential-type potentials Diatomic molecules 



This work was partially supported by the projects UAM-A-CBI-2232004 and 009. One of us (JGR) thanks the Instituto Politécnico Nacional for the financial support given through the COFAA-IPN project SIP-20180062. We are grateful with the SNI - Conacyt - México for the stipend received.


  1. 1.
    Arai A (1991) J Math Anal Appl 158:63CrossRefGoogle Scholar
  2. 2.
    Eğrifes H, Demirhan D, Büyükkılıç F (2000) Phys Lett A 275:229CrossRefGoogle Scholar
  3. 3.
    Eğrifes H, Demirhan D, Büyükkılıç F (1999) Phys Scr 59:90CrossRefGoogle Scholar
  4. 4.
    Eğrifes H, Demirhan D, Büyükkılıç F (1999) Phys Scr 60:195CrossRefGoogle Scholar
  5. 5.
    Jia CS et al (2002) Phys Lett A 294:185CrossRefGoogle Scholar
  6. 6.
    Jia CS et al (2002) Phys Lett A 298:78CrossRefGoogle Scholar
  7. 7.
    Jia CS et al (2002) Phys Lett A 300:115CrossRefGoogle Scholar
  8. 8.
    Jia CS et al (2002) Phys Lett A 305:231CrossRefGoogle Scholar
  9. 9.
    Setare MR, Fallahpour A (2009) Int J Theor Phys 49:1263CrossRefGoogle Scholar
  10. 10.
    Yılmaz H, Demirhan D, Büyükkılıç F (2010) J Math Chem 47:539CrossRefGoogle Scholar
  11. 11.
    Falaye BJ, Oyewumi KJ, Abbas M (2013) Chin Phys B 22:110301CrossRefGoogle Scholar
  12. 12.
    Suparmi A, Cari C, Yuliani H (2013) Adv Phys Theor Appl 16:64Google Scholar
  13. 13.
    Eshghi M, Meharaban M, Ghafoori M (2017) Math Methods Appl Sci 40:10003CrossRefGoogle Scholar
  14. 14.
    Sebawe Abdalla M, Eleuch H (2014) J Appl Phys 115:234906CrossRefGoogle Scholar
  15. 15.
    Sari RA, Suparmi A, Cari C (2016) Chin Phys B 25:010301CrossRefGoogle Scholar
  16. 16.
    Peña JJ, Ovando G, Morales J, García-Ravelo J (2017) J Mol Model 23:265CrossRefGoogle Scholar
  17. 17.
    Peña JJ, García-Ravelo J, Morales J (2017) Journal of Mathematical Physics 58:043501CrossRefGoogle Scholar
  18. 18.
    de Souza Dutra A (2005) Phys. Lett. A. 339:252CrossRefGoogle Scholar
  19. 19.
    Abramowitz M, Stegun IA (1972) Handbook of Mathematical Functions, National Bureau of Standards, Applied Mathematics Series—55, Washington, DC 20402Google Scholar
  20. 20.
    Berkdemir C, Berkdemir A, Sever R (2005) Phys Rev C 72:027001CrossRefGoogle Scholar

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CBI - Area de Física Atómica Molecular AplicadaUniversidad Autónoma Metropolitana - AzcapotzalcoMexico CityMexico
  2. 2.Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional - Zacatenco, Edificio 9Unidad Profesional Adolfo López MateosMexico CityMexico
  3. 3.División de Ingeniería BiomédicaTecnológico de Estudios Superiores de IxtapalucaIxtapalucaMexico

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