Two-Electron Spherical Quantum Dot in a Magnetic Field

A Poszwa

doi:10.1007/s00601-016-1138-5

Abstract

We investigate three-dimensional, two-electron quantum dots in an external magnetic field B. Due to mixed spherical and cylindrical symmetry the Schrodinger equation is not completely separable. Highly accurate numerical solutions, for a wide range of B, have been obtained by the expansion of wavefunctions in double-power series and by imposing on the radial functions appropriate boundary conditions. The asymptotic limit of a very strong magnetic field and the 2D approach have been considered. Ground state properties of the two-electron semiconductor quantum dots are investigated using both the 3D and 2D models. Theoretical calculations have been compared with recent experimental results.

Highlights

The influence of spatial confinement on properties of quantum systems have been widely studied in the literature and remains subject of continuous interest in both theoretical and experimental fields [1,2,3,4,5]
We have introduced above the eigenvalue E and following parameters s=
Writing the total wavefunction of two electrons as Ψ (1, 2) = Ψc.m.(R)ψ(r)χ (1, 2) we can find that the operation of exchanging two electrons leads to Ψ (2, 1) = Ψc.m.(R)ψ(−r)χ (2, 1)

Summary

Introduction

The influence of spatial confinement on properties of quantum systems have been widely studied in the literature and remains subject of continuous interest in both theoretical and experimental fields [1,2,3,4,5]. The HA refers to a model system composed of two electrons interacting by the Coulombic potential and confined in an external harmonic potential. Many applications for this system ensues from some unique properties of the HA. For the HA the Schrödinger equation separates exactly and, for a set of the coupling constants, closed-form analytical solutions exist [9,10]. This is of particular importance for the understanding of the role of electron–electron interaction and correlation effects

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