Related papers: Experiment and Theory in Computations of the He At…
Based on the Schrodinger equation, exact expressions for the non-relativistic particle energy in the local external field and the external field potential are derived as inhomogeneous density functionals. On this basis, it is shown that,…
We treat a system (a molecule or a solid) in which electrons are coupled linearly to any number and type of harmonic oscillators and which is further subject to external forces of arbitrary symmetry. With the treatment restricted to the…
We present exact explicit analytical results describing the exact ground state of four electrons in a two dimensional square Hubbard cluster containing 16 sites taken with periodic boundary conditions. The presented procedure, which works…
In this article, we derived a rigorous lower bound on the ground-state energy for a class of one-dimensional quantum systems in deformed space with minimal coordinate and momentum uncertainties, representing the absolute minimum energy that…
Entanglement may be considered a resource for quantum-information processing, as the origin of robust and universal equilibrium behaviour, but also as a limit to the validity of an effective potential approach, in which the influence of…
Helium (He) is the ideal atom to perform tests of ab-initio calculations in two-electron systems that consider all known effects, including quantum-electrodynamics and nuclear-size contributions. Recent state-of-the-art calculations and…
The triplet contribution is computed to the 1 and 2 $^1S^\text{e}_0$ states of the He atom, to the $1\ ^1S^\text{e}_0$ state of the Li$^+$ and Be${^{2+}}$ ions, and to the $X\ ^1\Sigma_\text{g}^+$ ground state of the H$_2$ molecule by…
In this work we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the…
We calculate the ground--state energy and other physical properties of the hydrogen atom inside a spherical box with an impenetrable wall. We apply the variational method and perturbation theory and compare both approximate results. We show…
The quantum mechanics of two-electron systems is reviewed, starting with the ground state of the helium atom and helium-like ions, with central charge $Z\ge 2$. For Z=1, demonstrating the stability of the negative hydrogen ion, H$^-$,…
With a super-high-efficient numerical algorithm, we are able to self-consistently calculate the Green's function in the renormalized-ring-diagram approximation for a two-dimensional electron system with long-range Coulomb interactions. The…
The nonrelativistic energies of the homonuclear ion T$_2^+$ are calculated for the ground state using the Lagrange-mesh method as was done for the isotopomers H$_2^+$ and D$_2^+$ ({\it J. Phys. B: At. Mol. Opt. Phys.} {\bf 45} 065101 and…
We have performed self-consistent calculations for first and second row atoms using a variant of density-functional theory, the optimized effective potential method, with an approximation due to Krieger, Li and Iafrate and a…
Some present day results for few-nucleon bound state, two-nucleon correlation functions and scattering observables are briefly reviewed. The old idea of the Coulomb sum rule as a way to extract the pp correlation function is reconsidered.…
A procedure is described for efficiently finding the ground state energy and configuration for a Frenkel-Kontorova model in a periodic potential, consisting of N parabolic segments of identical curvature in each period, through a numerical…
Results of our recent highly accurate computations of the Coulomb two-center systems with the unit electrical charges $X^{+} X^{+} e^{-}$ and $X^{+} Y^{+} e^{-}$ are discussed. In particular, we have determined (to very high accuracy) the…
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…
The non-relativistic electronic Hamiltonian, H(a)= Hkin + Hne + aHee, extended with coupling strength parameter (a), allows to switch the electron-electron repulsion energy off and on. First, the easier a=0 case is solved and the solution…
The continuum of $^{10}$He nucleus is studied theoretically in a three-body $^{8}$He+$n$+$n$ model basing on the recent information concerning $^9$He spectrum [Golovkov, \textit{et al.}, Phys. Rev. C \textbf{76}, 021605(R) (2007)]. The…
We compute the energy spectrum of the ground state of a 2D Dirac electron in the presence of a Coulomb potential and a constant magnetic field perpendicular to the plane where the the electron is confined. With the help of a mixed-basis…