Exciton states in a quantum dot with parabolic confinement

Abstract

In this study the electronic eigenstructure of an exciton in a parabolic quantum dot (QD) has been calculated with a high accuracy by using Finite element method (FEM). We have converted the coordinates of electronlight-hole system to relative and center of mass coordinate, then placed the Spherical Harmonics into Schrödinger equation analytically and obtained the Schrödinger equation which depends only on the radial variable. Finally we used FEM with only radial variable in order to get the accurate numerical results. We also showed first 21 energy level spectra of exciton depending on confinement and Coulomb interaction parameters