skip to main content

SciTech ConnectSciTech Connect

Title: Solving a two-electron quantum dot model in terms of polynomial solutions of a Biconfluent Heun equation

The effects on the non-relativistic dynamics of a system compound by two electrons interacting by a Coulomb potential and with an external harmonic oscillator potential, confined to move in a two dimensional Euclidean space, are investigated. In particular, it is shown that it is possible to determine exactly and in a closed form a finite portion of the energy spectrum and the associated eigenfunctions for the Schrödinger equation describing the relative motion of the electrons, by putting it into the form of a biconfluent Heun equation. In the same framework, another set of solutions of this type can be straightforwardly obtained for the case when the two electrons are submitted also to an external constant magnetic field. - Highlights: • Exact solution of a quantum dot model. • Determination of the energy levels. • Investigation of how the radial wave functions depend on the external excitation frequency. • Characteristic length between the two-electrons are found to be compatible with the semiconductor lattice parameter.
Authors:
 [1] ;  [2] ; ;  [3]
  1. Centro Brasileiro de Pesquisas Físicas - Rua Dr. Xavier Sigaud, 150, 22290-180, Urca, Rio de Janeiro, RJ (Brazil)
  2. (Brazil)
  3. Instituto de Física Armando Dias Tavares, Universidade do Estado do Rio de Janeiro - Rua São Francisco Xavier, 524, 20550-900, Maracanã, Rio de Janeiro, RJ (Brazil)
Publication Date:
OSTI Identifier:
22447578
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 347; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COULOMB FIELD; EIGENFUNCTIONS; ELECTRONS; ENERGY SPECTRA; EUCLIDEAN SPACE; HARMONIC OSCILLATORS; POLYNOMIALS; QUANTUM DOTS; SCHROEDINGER EQUATION