Related papers: Quasi Sturmian Basis in Two-Electron Continuum Pro…
We give a detailed account of an $\it{ab}$ $\it{initio}$ spectral approach for the calculation of energy spectra of two active electron atoms in a system of hyperspherical coordinates. In this system of coordinates, the Hamiltonian has the…
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…
In the framework of the study of helium-like atomic systems possessing the collinear configuration, we propose a simple method for computing compact but very accurate wave functions describing the relevant $S$ state. It is worth noting that…
A simple method of variational calculations of the electronic structure of a two-electron atom/ion, primarily near the nucleus, is proposed. The method as a whole consists of a standard solution of a generalized matrix eigenvalue equation,…
The limit relations for the partial derivatives of the two-electron atomic wave functions at the two-particle coalescence lines have been obtained numerically using accurate CFHHM wave functions. The asymptotic solutions of the proper…
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$^-$,…
As a step toward the full \emph{ab-initio} description of two-photon double ionization processes, we present a finite-pulse version of the virtual-sequential model for polyelectronic atoms. The model relies on the \emph{ab initio}…
Collinear configurations of the helium-like atomic systems, relevant, e.g., for the quasifree mechanism of the double photoionization of helium, are studied, parameterized by the single scalar parameter $-1\leq \lambda\leq1$ ("collinear…
The form of the wave function at three-electron coalescence points is examined for several spin states using an alternative method to the usual Fock expansion. We find that, in two- and three-dimensional systems, the non-analytical nature…
The first discussion of basis sets consisting of exponentially decaying Coulomb Sturmian functions for modelling electronic structures is presented. The proposed basis set construction selects Coulomb Sturmian functions using separate upper…
The exactly solvable model of quasi-conical quantum dot, having a form of spherical sector is proposed. Due to the specific symmetry of the problem the separation of variables in spherical coordinates is possible in the one-electron…
We find approximate analytical presentation of the solutions $\Psi(r_1, r_2, r_{12})$ of Schr\"odinger equation for two-electron system bound by the nucleus, in the space region $r_{1,2}=0$ and $r_{12}=0$ that are of great importance for a…
The non-relativistic interacting electron gas in an external field of positively charged massive cores is dealt with in the scheme of second quantization. Ladder operators that change between stationary states of contiguous energy…
Formulas and expectation values which are need to determine the lowest-order QED corrections ($\sim \alpha^3$) and corresponding recoil (or finite mass) corrections in the two-electron helium-like ions are presented. Other important…
In this work we give a comprehensive derivation of an exact and numerically feasible method to perform ab-initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierachy of…
A method for determining the ground state of a planar interacting many-electron system in a magnetic field perpendicular to the plane is described. The ground state wave-function is expressed as a linear combination of a set of basis…
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.…
We discuss two different types of issues concerning the quantization of Einstein-Rosen waves. First of all we study in detail the possibility of using the coherent states corresponding to the dynamics of the auxiliary, free Hamiltonian…
We present analytical solutions to a quantum-mechanical three-body problem in three dimensions, which describes a helium-like two-electron atom. Similarly to Hooke's atom, the Coulombic electron-nucleus interaction potentials are replaced…
We define Sturmian basis functions for the harmonic oscillator and investigate whether recent insights into Sturmians for Coulomb-like potentials can be extended to this important potential. We also treat many body problems such as coupling…