Symbolic-numeric algorithms for computer analysis of spheroidal quantum dot models

Authors:
A. A. Gusev;O. Chuluunbaatar;V. P. Gerdt;V. A. Rostovtsev;S. I. Vinitsky;V. L. Derbov
Affiliations:
Joint Institute for Nuclear Research, Dubna, Russia and Dubna International University of Nature, Society & Man, Dubna, Russia;Joint Institute for Nuclear Research, Dubna, Russia;Joint Institute for Nuclear Research, Dubna, Russia;Joint Institute for Nuclear Research, Dubna, Russia and Dubna International University of Nature, Society & Man, Dubna, Russia;Saratov State University, Saratov, Russia;Saratov State University, Saratov, Russia
Venue:
CASC'10 Proceedings of the 12th international conference on Computer algebra in scientific computing
Year:
2010

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Abstract

A computational 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.