Two interacting electrons in a magnetic field: comparison of semiclassical, quantum, and variational solutions

TL;DR

This paper compares quantum, semiclassical, and variational methods for analyzing two interacting electrons in a magnetic field, providing insights into their energy spectra and dynamics in two-dimensional nanodevices.

Contribution

It introduces a comprehensive comparison between exact quantum solutions, semiclassical approximations, and variational approaches for a two-electron system in a magnetic field.

Findings

Quantum and semiclassical spectra show good agreement.

Variational method captures key dynamical features.

Insights applicable to nanodevice electron behavior.

Abstract

The quantum mechanical many-body problem is rarely analytically solvable. One notable exception is the case of two electrons interacting via a Coulomb potential in a uniform magnetic field. The motion is confined to a two-dimensional plane, which is commonly the case in nanodevices. We compare the exact solution with the semiclassical energy spectrum and study the time-dependent dynamics of the system using the time-dependent variational principle.