Computer algebra in nanosciences: Modeling electronic states in quantum dots

Dmytro Chibisov, Victor Ganzha, Sergey Pankratov, Christoph Zenger

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In the present paper we discuss single-electron states in a quantum dot by solving the Schrödinger equation taking into account spatial constraints, in which the confinement is modeled by a spherical potential wall (particle-in-a-sphere model). After the separation of variables we obtain second order ordinary differential equations, so that automatic methods for finding a closed-form solution are needed. We present a symbolic algorithm implemented in Maple based on the method of indeterminate coefficients, which reduces the obtained equations to the well-known differential equations. The latter can be solved in terms of hypergeometric or Bessel functions. The usage of indeterminate coefficients allows one to obtain the solution of the problem equations in terms of control parameters, which can then be choosen according to the purposes of a nanotechological process.

Original languageEnglish
Title of host publicationComputer Algebra in Scientific Computing - 8th International Workshop, CASC 2005, Proceedings
Pages115-124
Number of pages10
DOIs
StatePublished - 2005
Event8th International Workshop on Computer Algebra in Scientific Computing, CASC 2005 - Kalamata, Greece
Duration: 12 Sep 200516 Sep 2005

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3718 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference8th International Workshop on Computer Algebra in Scientific Computing, CASC 2005
Country/TerritoryGreece
CityKalamata
Period12/09/0516/09/05

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