Related papers: Explicitly correlated Helium wave function and hyp…
Helium atom is the simplest many-body electronic system provided by nature. The exact solution to the Schr\"odinger equation is known for helium ground and excited states, and represents a workbench for any many-body methodology. Here, we…
We study dissipation effects for electrons on the surface of liquid helium, which may serve as qubits of a quantum computer. Each electron is localized in a 3D potential well formed by the image potential in helium and the potential from a…
We discuss a method of solving the time dependent Schrodinger equation for atoms with two active electrons in a strong laser field, which we used in a previous paper [A. Scrinzi and B. Piraux, Phys. Rev. A 56, R13 (1997)] to calculate…
We propose some extensions of the quark potential model to hybrids, fit them to the lattice data and use them for the purpose of calculating the masses, root mean square radii and wave functions at the origin of the conventional and hybrid…
The helium ground state nonrelativistic energy with 24 significant digits is presented. The calculations are based on variational expansion with randomly chosen exponents. This data can be used as a benchmark for other approaches for many…
The Fourier component of the potential energy of interaction of an atom with an atom is represented as a polynomial of the fourth degree from the atomic form factor. A numerical calculation was performed for the atomic form factor in the…
An infinite sequence of potential well functions is considered. A trial wavefunction is used with the Schr$\ddot{\text{o}}$dinger equation to obtain an approximate ground state energy for each potential well function. We obtain an…
Based on an exposition of the underlying physics and applied mathematics in arXiv:1603.00899, this paper in five separate parts presents a description of the properties of the amplitude functions of the hydrogen atom according to wave…
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…
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…
Quantum mechanical scalar particle with polarizability is considered in the presence of the Coulomb field. Separation of variables is performed with the use of Wigner $D$-functions, the radial system of 15 equations is reduced to a single…
The correlation energies of the helium isoelectronic sequence and of Hooke's atom isoelectronic sequence have been evaluated using an assortment of local, gradient and meta-gradient density functionals. The results are compared with the…
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…
The critical nuclear charge Zc required for a heliumlike atom to have at least one bound state was recently determined with high accuracy from variational calculations. Analysis of the wave functions further suggested that the bound state…
We generalize the known solution of the Schr\"odinger equation, describing a particle confined to a triangular area, for a triangular graphene quantum dot with armchair-type boundaries. The quantization conditions, wave functions, and the…
Double photo-electron momentum spectra of the Helium atom are calculated \textit{ab initio} at extreme ultra-violet and near infrared wavelengths. At short wavelengths two-photon double ionization yields, two-electron energy spectra, and…
Fully numerical mesh solutions of 2D and 3D quantum equations of Schroedinger and Hartree-Fock type allow us to work with wavefunctions which possess a very flexible geometry. This flexibility is especially important for calculations of…
We study the numerical solution of the non-relativistic Schr\"{o}dinger equation for two-electron atoms in ground and excited S-states using pseudospectral (PS) methods of calculation. The calculation achieves convergence rates for the…
The renewed Green's function approach to calculating the angular Fock coefficients, $\psi_{k,p}(\alpha,\theta)$ is presented. The final formulas are simplified and specified to be applicable for analytical as well as numerical calculations.…
A powerful approach to solve the Coulombic quantum three-body problem is proposed. The approach is exponentially convergent and more efficient than the Hyperspherical Coordinate(HC) method and the Correlation Function Hyperspherical…