Accurate solution of the eigenvalue problem for some systems of ODE for calculating holes states in polynomial quantum wells

Accurate solution of the eigenvalue problem for some systems of ODE for calculating holes states in polynomial quantum wells

We demonstrate an explicit numerical method for accurate solving the eigenvalue problem for some systems of ordinary differential equations, in particular, those describing electron and hole bound states in semiconductor quantum wells with polynomial potential profiles. Holes states are described by...

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Main Authors: A Polupanov, S Evdochenko
Format: Article
Language:English
Published: Multi-Science Publishing 2016-09-01
Series:International Journal of Multiphysics
Online Access:http://journal.multiphysics.org/index.php/IJM/article/view/236
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spelling doaj-5258bd508dad46ada8ee18ff6f52f7c12020-11-24T22:41:34ZengMulti-Science PublishingInternational Journal of Multiphysics1750-95482048-39612016-09-017310.1260/1750-9548.7.3.219248Accurate solution of the eigenvalue problem for some systems of ODE for calculating holes states in polynomial quantum wellsA Polupanov0S Evdochenko1Kotel’nikov Institute of Radio-Engineering and Electronics of the Russian Academy of Sciences, Mokhovaya 11/7, 125009, Moscow, Russia Moscow City University of Psychology and Education, Sretenka, 29, Moscow, RussiaMoscow City University of Psychology and Education, Sretenka, 29, Moscow, RussiaWe demonstrate an explicit numerical method for accurate solving the eigenvalue problem for some systems of ordinary differential equations, in particular, those describing electron and hole bound states in semiconductor quantum wells with polynomial potential profiles. Holes states are described by the Luttinger Hamiltonian matrix. For solving the eigenvalue problem we use the recurrent sequences procedure that makes possible to derive exact analytical expression for the eigenfunctions,. Hole bound states energies and corresponding wave functions are calculated in a finite parabolic quantum well as functions of the lateral quasimomentum component and parameters of the potential.http://journal.multiphysics.org/index.php/IJM/article/view/236
collection DOAJ
language English
format Article
sources DOAJ
author A Polupanov
S Evdochenko
spellingShingle A Polupanov
S Evdochenko
Accurate solution of the eigenvalue problem for some systems of ODE for calculating holes states in polynomial quantum wells
International Journal of Multiphysics
author_facet A Polupanov
S Evdochenko
author_sort A Polupanov
title Accurate solution of the eigenvalue problem for some systems of ODE for calculating holes states in polynomial quantum wells
title_short Accurate solution of the eigenvalue problem for some systems of ODE for calculating holes states in polynomial quantum wells
title_full Accurate solution of the eigenvalue problem for some systems of ODE for calculating holes states in polynomial quantum wells
title_fullStr Accurate solution of the eigenvalue problem for some systems of ODE for calculating holes states in polynomial quantum wells
title_full_unstemmed Accurate solution of the eigenvalue problem for some systems of ODE for calculating holes states in polynomial quantum wells
title_sort accurate solution of the eigenvalue problem for some systems of ode for calculating holes states in polynomial quantum wells
publisher Multi-Science Publishing
series International Journal of Multiphysics
issn 1750-9548
2048-3961
publishDate 2016-09-01
description We demonstrate an explicit numerical method for accurate solving the eigenvalue problem for some systems of ordinary differential equations, in particular, those describing electron and hole bound states in semiconductor quantum wells with polynomial potential profiles. Holes states are described by the Luttinger Hamiltonian matrix. For solving the eigenvalue problem we use the recurrent sequences procedure that makes possible to derive exact analytical expression for the eigenfunctions,. Hole bound states energies and corresponding wave functions are calculated in a finite parabolic quantum well as functions of the lateral quasimomentum component and parameters of the potential.
url http://journal.multiphysics.org/index.php/IJM/article/view/236
work_keys_str_mv AT apolupanov accuratesolutionoftheeigenvalueproblemforsomesystemsofodeforcalculatingholesstatesinpolynomialquantumwells
AT sevdochenko accuratesolutionoftheeigenvalueproblemforsomesystemsofodeforcalculatingholesstatesinpolynomialquantumwells
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