Symbolic-Numeric Algorithms for Computer Analysis of Spheroidal Quantum Dot Models

Details Symbolic-Numeric Algorithms for Computer Analysis of Spheroidal Quantum Dot Models Symbolic-Numeric Algorithms for Computer Analysis of Spheroidal Quantum Dot Models

2010-04-23

arxiv.org/abs/1004.4202v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

6 figures, Submitted to Proc. of The 12th International Workshop on Computer Algebra in Scientific Computing (CASC 2010) Tsakh

Scientific paper

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.

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