Symbolic-Numeric Algorithms for Computer Analysis of Spheroidal Quantum Dot Models
Abstract
A computation scheme for solving elliptic boundary value problems with axially symmetric confining potentials using different sets of one-parameter basis functions is presented. The efficiency of the proposed symbolic-numerical algorithms implemented in Maple is shown by examples of spheroidal quantum dot models, for which energy spectra and eigenfunctions versus the spheroid aspect ratio were calculated within the conventional effective mass approximation. Critical values of the aspect ratio, at which the discrete spectrum of models with finite-wall potentials is transformed into a continuous one in strong dimensional quantization regime, were revealed using the exact and adiabatic classifications.
Cite
@article{arxiv.1004.4202,
title = {Symbolic-Numeric Algorithms for Computer Analysis of Spheroidal Quantum Dot Models},
author = {A. A. Gusev and O. Chuluunbaatar and V. P. Gerdt and V. A. Rostovtsev and S. I. Vinitsky and V. L. Derbov and V. V. Serov},
journal= {arXiv preprint arXiv:1004.4202},
year = {2015}
}
Comments
6 figures, Submitted to Proc. of The 12th International Workshop on Computer Algebra in Scientific Computing (CASC 2010) Tsakhkadzor, Armenia, September 5 - 12, 2010