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Publisher DOI: 10.1016/j.cpc.2005.12.003
Title: Numerical calculation of the electronic structure for three-dimensional quantum dots
Language: English
Authors: Voß, Heinrich 
Keywords: quantum dot;nonlinear eigenproblem;Schrödinger equation;Rayleigh functional;computer simulation
Issue Date: Aug-2005
Source: Preprint. Published in: Computer Physics CommunicationsVolume 174, Issue 6, 15 March 2006, Pages 441-446
Part of Series: Preprints des Institutes für Mathematik 
Volume number: 91
Abstract (english): 
In some recent papers Li, Voskoboynikov, Lee, Sze and Tretyak suggested an iterative scheme for computing the electronic states of quantum dots and quantum rings taking into account an electron effective mass which depends on the position and electron energy level. In this paper we prove that this method converges globally and linearly in an alternating way, i.e. yielding lower and upper bounds of a predetermined energy level in turn. Moreover, taking advantage of the Rayleigh functional of the governing nonlinear eigenproblem, we propose a variant which converges even quadratically thereby reducing the computational cost substantially. Two examples of finite element models of quantum dots of different shapes demonstrate the efficiency of the method.
DOI: 10.15480/882.58
Institute: Mathematik E-10 
Document Type: Preprint
License: In Copyright In Copyright
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