Related papers: Ground state of two electrons on a sphere
We analyze a model problem representing a multi-electronic molecule sitting on a metal surface. Working with a reduced configuration interaction Hamiltonian, we show that one can extract very accurate ground state wavefunctions as compared…
We calculate the Hartree-Fock energy of a density-wave in a spin polarized two-dimensional electron gas using a short-range repulsive interaction. We find that the stable ground state for a short-range potential is always either the…
The energy levels of two interacting electrons in a 2D quantum dot confined by a finite Gaussian potential and subjected to a uniform magnetic field perpendicular to the plane of the dot are studied. Analytic results are obtained for the…
We calculate the ground state phase diagram of the homogeneous electron gas in two dimensions within the Hartree-Fock approximation. At high density, we find stable solutions, where the electronic charge and spin density form an…
It is shown for two electron atoms that ground-state wavefunctions of the form \begin{equation} \Psi(\vec{r_{1}}, \vec{r_{2}})=\phi(\vec{r_{1}})\phi(\vec{r_{2}})(\cosh ar_{1}+\cosh ar_{2})(1+0.5 r_{12}e^{-b r_{12}}) \end{equation} where…
We calculate ground state energies in the Brueckner-Hartree-Fock theory for $N$ electrons (with $N\le 20$) confined to a circular quantum dot and in presence of a static magnetic field. Comparison with the predictions of Hartree-Fock,…
We explore the existence and behaviour of holomorphic restricted Hartree-Fock (h-RHF) solutions for two-electron problems. Through algebraic geometry, the exact number of solutions with $n$ basis functions is rigorously identified as…
Generalizing the classical Thomson problem to the quantum regime provides an ideal model to explore the underlying physics regarding electron correlations. In this work, we systematically investigate the combined effects of the geometry of…
We test a set of multiconfigurational wavefunction approaches for calculating the ground state electron population for a two-site Anderson model representing a molecule on a metal surface. In particular, we compare (i) a Hartree Fock like…
We study electronic structures of quasi-two-dimensional finite electron systems in high magnetic fields. The solutions in the fractional quantum Hall regime are interpreted as quantum liquids of electrons and off-electron vortices. The…
We investigate, both analytically and numerically, the behavior of the electron gas on a sphere in the presence of point-like impurities. We find a criterion when the disorder can be regarded as small one and the main effect is the…
We introduce an energy functional for ground-state electronic structure calculations. Its variables are the natural spin-orbitals of singlet many-body wave functions and their joint occupation probabilities deriving from controlled…
A new electronic structure model is developed in which the ground state energy of a molecular system is given by a Hartree-Fock-like expression with parametrized one- and two-electron integrals over an extended (minimal + polarization) set…
The exact ground state of four electrons in an arbitrary large two leg Hubbard ladder is deduced from nine analytic and explicit linear equations. The used procedure is described, and the properties of the ground state are analyzed. The…
We study the ground state and the collective excitations of parabolically-confined double-layer quantum dot systems in a strong magnetic field. We identify parameter regimes where electrons form maximum density droplet states, quantum-dot…
A simple expression for a ground state energy for a two-electron atom is derived. For this, assumption based upon the Niels Bohr ''old'' quantum mechanics idea about electron correlation in a two-electron atom is exploited. Results are…
By introducing a phase field and solving the eigen-functional equation of particles, we obtain the exact expressions of the ground state energy as a functional of the particle density for interacting electron/boson systems, and a…
Calculations for two electrons in an elliptic quantum dot, using symmetry breaking at the unrestricted Hartree-Fock level and subsequent restoration of the broken parity via projection techniques, show that the electrons can localize and…
With a generic lattice model for electrons occupying a semi-infinite crystal with a hard surface, we study the eigenstates of the system with a bulk band gap (or the gap with nodal points). The exact solution to the wave functions of…
A Hartree--Fock analysis of the ground-state electronic structure of the finite spherical jellium model is carried out for systems containing up to $520$ electrons in a positive background field with densities ranging from $10^{-3}$ to $1$.…