On the symmetry of the electronic density in the three-electron parabolic quantum dot

TL;DR

This paper investigates the approximate symmetry of electronic density in triplet states of a three-electron parabolic quantum dot, revealing that potential energy symmetry near its minimum causes this, which may aid in variable separation in quantum dot models.

Contribution

It demonstrates the origin of symmetry in electronic density of three-electron quantum dots and suggests implications for solving the Schrödinger equation.

Findings

Electronic density of triplet states shows approximate symmetry.

Symmetry is caused by potential energy symmetry near its minimum.

Insights into variable separation in quantum dot Schrödinger equations.

Abstract

The structure of the lowest states of a three-electron axially symmetric parabolic quantum dot in a zero magnetic field is investigated. It is shown that the electronic density of the triplet states possesses certain approximate symmetry which is best seen when using Dalitz plots as the visualization tool. It is demonstrated that the origin of that symmetry is caused by the symmetry of the potential energy in the vicinity of its minimum. The discovered symmetry could provide an insight into the problem of the separation of slow and fast variables in the Schro\"dinger equation for the axially or spherically symmetric quantum dots.