Related papers: Explicitly correlated Helium wave function and hyp…
A detailed analysis on the effect of spherical impenetrable confinement on the structural properties of two-electron ions in S-states have been done. The energy values of 1sns [n = 2-4] (3Se) states of helium-like ions (Z = 2-5) are…
In Part one of this Paper a hypothesis is forwarded of the electron charge in an atom existing in a distributed form. To check it by methods of electrodynamics and mechanics (without invoking the formalism of quantum mechanics and the…
Quantum theory has been remarkably successful in providing an understanding of physical systems at foundational scales. Solving the Schr\"odinger equation provides full knowledge of all dynamical quantities of the physical system. However…
We have calculated the ground state electronic structure of He under pressure from 0 to 1500 GPa using both all-electron full-potential and pseudopotential methods based on the density functional theory (DFT). We find that throughout this…
The energy eigenvalues and the wave functions of an $\alpha$ particle in a Bohrium $270$ nucleus were calculated by solving Schr\"odinger equation for Generalized Symmetric Woods-Saxon potential. Using the energy spectrum by excluding and…
The standard solution of the Schroedinger equation for the hydrogen atom is analyzed. Comparing with the recently established internal properties of electrons it is found, that these solutions cannot be seen as physically valid states of…
We study the hierarchical wave functions on a sphere and on a torus. We simplify some wave functions on a sphere or a torus using the analytic properties of wave functions. The open question, the construction of the wave function for…
We discuss the solutions of the Schroedinger equation for piecewise potentials, given by the harmonic oscillator potential for $\vert x\vert >a$ and an arbitrary function for $\vert x\vert <a$, using elementary methods. The study of this…
A trial wave function for two-dimensional quantum dot helium in an arbitrary perpendicular magnetic field (a system of two interacting electrons in a two-dimensional parabolic confinement potential) is introduced. A key ingredient of this…
The energetically lowest five states of a helium atom are: He($1^1S$), He($2^3S$), He($2^1S$), He($2^3P$), and He($2^1P$). Long-range interaction coefficients $C_3$, $C_6$, $C_8$, $C_9$, and $C_{10}$ for all $S-S$ and $S-P$ pairs of these…
A new heuristic model of interaction of an atomic system with a gravitational wave is proposed. In it, the gravitational wave alters the local electromagnetic field of the atomic nucleus, as perceived by the electron, which changes the…
In this article we are going to study the FEM solution to the Density Functional description of Helium. Solving self-consistently including electron-electron repulsion and exchange-correlation effects. This project will be split in four…
We have calculated the total energy of the helium atom in higher excited state. The Coulomb and exchange integrals are evaluated via spherical harmonics. The interaction of the magnetic moments of the electrons between them and also with…
Recent measurements of the ionization energies of the Rydberg $^1P$ states of helium for principal quantum number $n = 24$ and higher present a new challenge to theoretical atomic physics. A long-standing obstacle to high precision atomic…
We present a fully {\it ab initio}, non-perturbative, time-dependent approach to describe single and double ionization of helium by proton and antiproton impact. A flexible and accurate finite-element discrete-variable-representation is…
The Schroedinger equation is solved for an A-nucleon system using an expansion of the wave function in nonsymmetrized hyperspherical harmonics. Our approach is both an extension and a modification of the formalism developed by Gattobigio et…
The pair potential for helium has been computed with accuracy improved by an order of magnitude relative to the best previous determination. For the well region, its uncertainties are now below 1 millikelvin. The main improvement is due to…
Isolated electrons resting above a helium surface are predicted to have a bound spectrum corresponding to a one-dimensional hydrogen atom. But in fact, the observed spectrum is closer to that of a quantum-defect atom. Such a model is…
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 analysis of correlation energy of the simplest first approximation of a variational method for the intrashell states of two-electron atoms is the purpose of the present work. This method allows to divide energy of atom on Coulomb and…