Related papers: Some remarks on the two-electron atom
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,…
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…
New sets of functions with arbitrary large finite cardinality are constructed for two-electron atoms. Functions from these sets exactly satisfy the Kato's cusp conditions. The new functions are special linear combinations of Hylleraas-…
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…
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…
A simple, seven-parameter trial function is proposed for a description of the ground state of the Lithium atom. It includes both spin functions. Inter-electronic distances appear in exponential form as well as in a pre-exponential factor,…
We formulate the calculation of the ground-state wavefunction and energy of a system of strongly correlated electrons in terms of scattering matrices. A hierarchy of approximations is introduced which results in an incremental expansion of…
A variational treatment for a two-electron quantum dot (the artificial helium atom) is proposed which leads to exact answer for the ground state energy. Depending on the magnetic field value the singlet-triplet and triplet-triplet…
Low-lying energy levels of two interacting electrons confined in a two-dimensional parabolic quantum dot in the presence of an external magnetic field have been revised within the frame of a novel model. The present formalism, which gives…
The two-electron self-energy contribution to the ground state energy of heliumlike ions is calculated both for a point nucleus and an extended nucleus in a wide interval of Z. All the two-electron contributions are compiled to obtain most…
Artificial molecular states of double quantum dots defined in bilayer graphene are studied with the atomistic tight-binding and its low-energy continuum approximation. We indicate that the extended electron wave functions have opposite…
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…
Two single-particle sources coupled in series to a chiral electronic waveguide can serve as a probabilistic source of two-particle excitations with tunable properties. The second-order correlation function, characterizing the state of…
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…
Wave functions of a new functional kind have been proposed for Helium-like atoms in this work . These functions explicitly depend on interelectronic and hyperspherical coordinates. The best ground state energy for the Helium atom $…
A framework for developing new approximate electronic structure methods is presented, in which the correlation energy of a many-electron system in the ground state is computed as in the single-reference second-order many-body perturbation…
Using an accurate semi-analytic wavefunction for two electron atoms, we construct the external potential for varying strength of electron-electron (e-e) interaction. Using this potential we explicitly calculate the energy of their positive…
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$^-$,…
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…
We have found a (dense) basis for the N-representable, two-electron densities, in which all N-representable two-electron densities can be expanded, using positive coefficients. The inverse problem of finding a representative wavefunction,…