Ground state of an exciton in a three-dimensional parabolic quantum dot: convergent perturbative calculation

TL;DR

This paper applies Turbiner's convergent perturbative method to accurately compute the ground state energy and wave function of an exciton in a 3D parabolic quantum dot, even under strong coupling conditions.

Contribution

It introduces a convergent perturbative approach that surpasses traditional methods in calculating exciton states in quantum dots, especially in strong coupling regimes.

Findings

Excellent agreement with numerical simulations across various parameters

Method effective in strong coupling regimes

Provides accurate ground state energies and wave functions

Abstract

Working in the effective-mass approximation, we apply a powerful convergent perturbative technique of Turbiner's to the calculation of the ground state energy and the wave function of an exciton confined to a three-dimensional parabolic quantum dot. Unlike the usual Rayleigh-Schrodinger perturbation theory, Turbiner's approach works well even in the regime of strong coupling and does not require the knowledge of the full solution to the undisturbed problem. The second-order convergent calculation presented below is in excellent agreement with the results of exact numerical simulations for a wide range of system's confinement parameters.