The review considers the peculiarities of symmetry breaking and symmetry transformations
and the related physical effects in finite quantum systems. Some types of symmetry in finite …

The problem of the Schrödinger equation for two electrons (interacting with Coulomb
potentials) in an external harmonic-oscillator potential is revisited and shown to be solvable …

It is generally believed that the old quantum theory, as presented by Niels Bohr in 1913, fails
when applied to few electron systems, such as the H2 molecule. Here we review recent …

Electrons can have a given smooth density distribution ρ (r), even if their Coulomb
interaction is scaled to infinity. This strong-interaction limit of density-functional theory …

We treat an analytically solvable version of the ''Hooke's Law''model for a two‐electron atom,
in which the electron–electron repulsion is Coulombic but the electron‐nucleus attraction is …

We show that the exact wave function for two electrons, interacting through a Coulomb
potential but constrained to remain on the surface of a D-sphere (D≥ 1), is a polynomial in …

Abstract According to Hohenberg-Kohn-Sham density-functional theory (DFT), and its
constrained search formulation, the Schrödinger ground-state wave function Ψ is a …

The recently developed concept of a correlation entropy, S, as a quantitative measure of the
correlation strength present in a correlated quantum many-body state is applied to the …

A commonly cited reason for the success of the local spin density (LSD) approximation is
that it correctly accounts for short wavelength contributions to the exchange-correlation …

We use the two-electron oscillator (with Coulomb interaction between the electrons) as a test
system for a selection of the most common one-particle approximations: Hartree-Fock (HF) …