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

TL;DR

This paper introduces symbolic-numeric algorithms implemented in Maple for analyzing spheroidal quantum dot models, calculating energy spectra and eigenfunctions, and identifying critical aspect ratios affecting the spectrum's nature.

Contribution

It presents a novel computation scheme combining symbolic and numerical methods for spheroidal quantum dots, including analysis of spectrum transitions with respect to aspect ratio.

Findings

Efficient algorithms for spheroidal quantum dot analysis

Identification of critical aspect ratios affecting spectrum

Calculation of energy spectra and eigenfunctions

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.