# Effective Hamiltonian for two-electron Quantum Dots from weak to strong parabolic confinement

## TL;DR

This paper develops an effective Hamiltonian model for two-electron quantum dots under varying confinement strengths, accurately capturing energy levels and the transition from molecular to atomic-like behavior.

## Contribution

It introduces a modified rovibrational Hamiltonian that effectively models the energy spectrum across weak to strong confinement regimes.

## Key findings

- Vibrational Hamiltonian accurately describes energy levels.
- Model reveals transition from molecular to atomic-like states.
- Modified Hamiltonian provides precise energy predictions.

## Abstract

We model quasi-two-dimensional two-electron Quantum Dots in a parabolic confinement potential with rovibrational and purely vibrational effective Hamiltonian operators. These are optimized by non-linear least-square fits to the exact energy levels. We find, that the vibrational Hamiltonian describes the energy levels well and reveals how relative contributions change on varying the confinement strength. The rovibrational model suggests the formation of a rigid two-electron molecule in weak confinement and we further present a modified model, that allows a very accurate transition from weak to strong confinement regimes.