Analytical and numerical calculations of spectral and optical characteristics of spheroidal quantum dots

TL;DR

This paper develops analytical and numerical methods to calculate the spectral and optical properties of spheroidal quantum dots, considering external electric fields, using perturbation theory within the effective mass approximation.

Contribution

It introduces perturbation theory schemes based on Kantorovich and adiabatic methods for spheroidal quantum dots, providing new analytical and numerical tools for spectral analysis.

Findings

Eigenvalues and eigenfunctions were obtained analytically and numerically.

Spectral and optical characteristics were analyzed under external electric fields.

The methods improve understanding of quantum dot behavior in applied fields.

Abstract

In the effective mass approximation for electronic (hole) states of a spheroidal quantum dot with and without external fields the perturbation theory schemes are constructed in the framework of the Kantorovich and adiabatic methods. The eigenvalues and eigenfunctions of the problem, obtained in both analytical and numerical forms, were applied for the analysis of spectral and optical characteristics of spheroidal quantum dots in homogeneous electric fields.