Comment on: “Bidimensional bound states for charged polar nanoparticles”

  • Paolo AmoreEmail author
  • Francisco M. Fernández
Brief Communication


In a recent paper, Castellanos-Jaramillo and Castellanos-Moreno proposed a simple quantum-mechanical model for an electron in the vicinity of an ionized nanostructure with a permanent electric dipole. They chose the interaction of the electron with the charge and the dipole in such a way that the resulting Schrödinger equation is separable into radial and angular parts. In this comment, we show that those authors did not solve the angular eigenvalue equation with proper periodic boundary conditions and that they also made a mistake in the elimination of the first derivative in the radial equation. Such errors invalidate their results of the Einstein coefficients for the \(\left (GaAs\right )_{3}\) system considered.


Nanoparticle model Two dimensions Schrödinger equation Rotational equation Radial equation 



Paolo Amore acknowledges support from Sistema Nacional de Investigadores (México)


  1. Castellanos-Jaramillo A, Castellanos-Moreno A (2019) Bidimensional bound states for charged polar nanoparticles. J Nanopart Res 21:141CrossRefGoogle Scholar
  2. Coon SA, Holstein BR (2002) Anomalies in quantum mechanics: the 1/r 2 potential. Am J Phys 70:513–519CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2020

Authors and Affiliations

  1. 1.Facultad de Ciencias, CUICBASUniversidad de ColimaColimaMexico
  2. 2.INIFTADivisión Química TeóricaLa PlataArgentina

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