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Confined orbitals in fullerenes and quantum dots calculated by analytic continuation method

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Abstract

The Schrödinger equation with a Gaussian potential to model a confined system as a quantum dot or a hydrogen atom inside a fullerene is solved by using the analytic continuation method. The use of the Rodrigues formula allows us to obtain in an easy way the coefficients of the power series expansion of the Gaussian potential in terms of the Hermite polynomials. Recurrence formulas have been obtained for the series of the states of one electron confined by that potential. This method is simpler and computationally more efficient than others employed to model quantum dots using Gaussian potentials.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The data appearing in the paper are those relevant for the results presented. No further data have been produced.]

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Acknowledgements

This work was partially supported by the Junta de Andalucía under grant FQM378 and the Universidad de Córdoba under a grant from the program “Plan Propio de Investigación 2019”. M.F.M.A. acknowledges partial support by a Ph.D fellowship from the Spanish Ministerio de Universidades under grant FPU16/05950.

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Authors and Affiliations

  1. Departamento de Física, Universidad de Córdoba, Campus de Rabanales, Edif. C2, 14071, Córdoba, Spain

    Milagros F. Morcillo-Arencibia, José Manuel Alcaraz-Pelegrina & Antonio J. Sarsa

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  1. Milagros F. Morcillo-Arencibia
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  2. José Manuel Alcaraz-Pelegrina
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  3. Antonio J. Sarsa
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All the authors were involved in the preparation of the manuscript. All the authors have read and approved the final manuscript.

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Correspondence to Antonio J. Sarsa.

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Morcillo-Arencibia, M.F., Alcaraz-Pelegrina, J.M. & Sarsa, A.J. Confined orbitals in fullerenes and quantum dots calculated by analytic continuation method. Eur. Phys. J. D 75, 109 (2021). https://doi.org/10.1140/epjd/s10053-021-00096-6

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  • DOI: https://doi.org/10.1140/epjd/s10053-021-00096-6

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