Solving Schrodinger Equation for Three-Electron Quantum Systems by the Use of The Hyperspherical Function Method

TL;DR

This paper introduces a hyperspherical function method to solve the Schrödinger equation for three-electron quantum dots in 2D, enabling analysis of ground states under magnetic fields with improved mathematical modeling.

Contribution

The paper develops a new mathematical model and applies the hyperspherical function method to accurately solve for ground states of three-electron quantum dots in magnetic fields.

Findings

Ground state energy levels as a function of magnetic field frequency

Separation of center of mass movement in the model

Effective use of logarithmic electron-electron interaction potential

Abstract

A new mathematical model for the description of three electron quantum dots in 2D space is created, and ground states of this system in external magnetic field is investigated. The Schrodinger equation for three two-dimensional electrons is solved by the use of the Hyperspherical Function Method (HFM) It is shown that the HFM allows us to separate the center of mass movement and solve Schrodinger Equation with the use of the logarithmic potential of electron-electron interactions. Ground state energy levels as function of the magnetic field frequency is obtained.