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Numerical Solutions for a Two-dimensional Quantum Dot Model

  • Atomic Physics
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Abstract

In this paper, a quantum dot mathematical model based on a two-dimensional Schrödinger equation assuming the 1/r inter-electronic potential is revisited. Generally, it is argued that the solutions of this model obtained by solving a biconfluent Heun equation have some limitations. The known polynomial solutions are confronted with new numerical calculations based on the Numerov method. A good qualitative agreement between them emerges. The numerical method being more general gives rise to new solutions. In particular, we are now able to calculate the quantum dot eigenfunctions for a much larger spectrum of external harmonic frequencies as compared to previous results. Also, the existence of bound state for such planar system, in the case ℓ = 0, is predicted and its respective eigenvalue is determined.

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Authors and Affiliations

  1. Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150, Urca, Rio de Janeiro, RJ, 22290-180, Brazil

    F. Caruso

  2. Instituto de Física Armando Dias Tavares, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier, 524, Maracanã, Rio de Janeiro, RJ, 20550-900, Brazil

    F. Caruso, V. Oguri & F. Silveira

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  1. F. Caruso
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  2. V. Oguri
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  3. F. Silveira
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Correspondence to F. Caruso.

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Caruso, F., Oguri, V. & Silveira, F. Numerical Solutions for a Two-dimensional Quantum Dot Model. Braz J Phys 49, 432–437 (2019). https://doi.org/10.1007/s13538-019-00656-7

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  • DOI: https://doi.org/10.1007/s13538-019-00656-7

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