Eigenstates and dynamics of Hooke’s atom: Exact results and path integral simulations

The system of two interacting electrons in one-dimensional harmonic potential or Hooke’s atom is considered, again. On one hand, it appears as a model for quantum dots in a strong confinement regime, and on the other hand, it provides us with a hard test bench for new methods with the “space splitti...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical physics 2018-05, Vol.59 (5)
Main Authors: Gholizadehkalkhoran, Hossein, Ruokosenmäki, Ilkka, Rantala, Tapio T.
Format: Article
Language:English
Subjects:
Computer simulation
Confinement
Coulomb potential
Dynamics
Eigenvalues
Eigenvectors
Electronic structure
Integral equations
Integrals
Perturbation theory
Quantum dots
Quantum physics
Simulation
Test procedures
Wave functions
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The system of two interacting electrons in one-dimensional harmonic potential or Hooke’s atom is considered, again. On one hand, it appears as a model for quantum dots in a strong confinement regime, and on the other hand, it provides us with a hard test bench for new methods with the “space splitting” arising from the one-dimensional Coulomb potential. Here, we complete the numerous previous studies of the ground state of Hooke’s atom by including the excited states and dynamics, not considered earlier. With the perturbation theory, we reach essentially exact eigenstate energies and wave functions for the strong confinement regime as novel results. We also consider external perturbation induced quantum dynamics in a simple separable case. Finally, we test our novel numerical approach based on real-time path integrals (RTPIs) in reproducing the above. The RTPI turns out to be a straightforward approach with exact account of electronic correlations for solving the eigenstates and dynamics without the conventional restrictions of electronic structure methods.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.5028503