Related papers: Two electrons in an external oscillator potential:…
The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is a physical example of quasi-exactly solvable systems. This model, however, does not belong to the classes based on the algebra…
We present a unified treatment of three cases of quasi-exactly solvable problems, namely, charged particle moving in Coulomb and magnetic fields, for both the Schr\"odinger and the Klein-Gordon case, and the relative motion of two charged…
We review our recent progress in the determination of the high-density correlation energy $\Ec$ in two-electron systems. Several two-electron systems are considered, such as the well known helium-like ions (helium), and the Hooke's law atom…
The classical dynamics of two electrons in the Coulomb potential of an attractive nucleus is chaotic in large parts of the high-dimensional phase space. Quantum spectra of two-electron atoms, however, exhibit structures which clearly hint…
The problem of two electrons in a two-dimensional random potential is addressed numerically. Specifically, the role of the Coulomb interaction between electrons on localization is investigated by writing the Hamiltonian on a localized basis…
The relation between certain Hamiltonians, known as dual, or partner Hamiltonians, under the transformation $x{\rightarrow}\bar{x}^{\bar{\alpha}}$ has long been used as a method of simplifying spectral problems in quantum mechanics. This…
We propose two generalisations of the Coulomb potential equation of quantum mechanics and investigate the occurence of algebraic eigenfunctions for the corresponding Scrh\"odinger equations. Some relativistic counterparts of these problems…
We extend the class of QM problems which permit for quasi-exact solutions. Specifically, we consider planar motion of two interacting charges in a constant uniform magnetic field. While Turbiner and Escobar-Ruiz (2013) addressed the case of…
The ordering of N equally charged particles (-e) moving in two dimensions and confined by a Coulomb potential, resulting from a displaced positive charge Ze is discussed. This is a classical model system for atoms. We obtain the…
We present a procedure to solve the Schroedinger equation of two interacting electrons in a quantum dot in the presence of an external magnetic field within the context of quasi-exactly-solvable spectral problems. We show that the…
We report analytic solutions of a recently discovered quasi-exactly solvable model consisting of two electrons, interacting {\em via} a Coulomb potential, but restricted to remain on the surface of a $\mathcal{D}$-dimensional sphere.…
The quantum mechanics of two Coulomb charges on a plane $(e_1, m_1)$ and $(e_2, m_2)$ subject to a constant magnetic field $B$ perpendicular to the plane is considered. Four integrals of motion are explicitly indicated. It is shown that for…
We study the semiclassical dynamics of interacting electrons in a biased crystal lattice. A complex dynamical scenario emerges from the interplay between the Coulomb and the external electric fields. When the electrons are far apart, the…
The effects on the non-relativistic dynamics of a system compound by two electrons interacting by a Coulomb potential and with an external harmonic oscillator potential, confined to move in a two dimensional Euclidean space, are…
Electron-electron correlation forms the basis of difficulties encountered in many-body problems. Accurate treatment of the correlation problem is likely to unravel some nice physical properties of matter embedded in this correlation. In an…
A Hubbard-type model is derived from the microscopic Schr\"odinger equation. We found that additional terms describing direct two-electron transitions must be added to the standard Hubbard Hamiltonian. Such a Hamiltonian generates…
Coulomb interactions that occur in electronic structure calculations are correlated by allowing basis function components of the interacting densities to polarize, thereby reducing the magnitude of the interaction. Exchange integrals of…
Two of the most iconic systems of quantum physics are the particle in a box and the Coulomb potential (the third is, of course, the harmonic oscillator). In this expository paper, we consider the quantum solution to the problem of an…
The all-order correlation potential method of accurate atomic structure calculations for atoms with one external electron is extended to include one more class of correlation diagrams to all orders. These are the so-called ladder diagrams…
The author suggests an approach based on the separation of total energy of multielectron systems into the semi-classical Coulomb part and the non-classical additional part. This approach allows on the one hand to simplify calculations and…