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A computation scheme for solving elliptic boundary value problems withaxially symmetric confining potentials using different sets of one-parameterbasis functions is presented. The efficiency of the proposed symbolic-numericalalgorithms implemented in Maple is shown by examples of spheroidal quantum dotmodels, for which energy spectra and eigenfunctions versus the spheroid aspectratio were calculated within the conventional effective mass approximation.Critical values of the aspect ratio, at which the discrete spectrum of modelswith finite-wall potentials is transformed into a continuous one in strongdimensional quantization regime, were revealed using the exact and adiabaticclassifications.

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