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On the q-deformed exponential-type potentials

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

Abstract

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.

Keywords

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

Notes

Acknowledgements

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.

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Copyright information

© 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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