@Article{CiCP-11-1591,
author = {Marta M. Betcke and Heinrich Voss},
title = {Analysis and Efficient Solution of Stationary Schrödinger Equation Governing Electronic States of Quantum Dots and Rings in Magnetic Field},
journal = {Communications in Computational Physics},
year = {2012},
volume = {11},
number = {5},
pages = {1591--1617},
abstract = {<p style="text-align: justify;">In this work the one-band effective Hamiltonian governing the electronic states of a quantum dot/ring in a homogenous magnetic field is used to derive a pair/quadruple of nonlinear eigenvalue problems corresponding to different spin orientations and in case of rotational symmetry additionally to quantum number ±ℓ. We show, that each of those pair/quadruple of nonlinear problems allows for the min-max characterization of its eigenvalues under certain conditions, which are satisfied for our examples and the common InAs/GaAs heterojunction. Exploiting the minmax property we devise efficient iterative projection methods simultaneously handling the pair/quadruple of nonlinear problems and thereby saving up to 40% of the computational time as compared to the nonlinear Arnoldi method applied to each of the problems separately.&nbsp;</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.110910.250511a},
url = {http://global-sci.org/intro/article_detail/cicp/7426.html}
}