Related papers: N-dimensional electron in a spherical potential: t…
We study hydrogen-like atoms in N=1 supersymmetric quantum electrodynamics with an electronic and a muonic family. These atoms are bound states of an anti-muon and an electron or their superpartners. The exchange of a photino converts…
A simple optimization scheme is used to compute the density-density response function of an electron liquid. Higher order terms in the perturbation expansion beyond the random phase approximation are summed approximately by enforcing the…
A few approximate schemes to solve the Hedin equations self-consistently introduced in (Phys. Rev. B 94, 155101 (2016)) are explored and tested for the 3D electron gas at metallic densities. We calculate one electron spectra, dielectric…
It is shown that, Baire generically, the bound states of the Hamiltonian of the Hydrogen atom have spectral measures with exact $0$-lower and $1/3$-upper generalized fractal dimensions; the relation to (a weak form of) dynamical…
We study the energy spectrum of the two-electron spherical parabolic quantum dot using the exact Schroedinger, the Hartree-Fock, and the Kohn-Sham equations. The results obtained by applying the shifted-1/N method are compared with those…
A technique to reconstruct one-dimensional, reflectionless potentials and the associated quantum wave functions starting from a finite number of known energy spectra is discussed. The method is demonstrated using spectra that scale like the…
Geometrical model for quantum objects is suggested. It is shown that equations for free material Dirac field and for Maxwell electromagnetic field can be considered as relations describing propagation of the space topological defects. This…
The hydrogen atom theory is developed for the de Sitter and anti de Sitter spaces on the basis of the Klein-Gordon-Fock wave equation in static coordinates. In both models, after separation of the variables, the problem is reduced to the…
Following a strong analogy with two-dimensional physics, the three-body pseudo-potential in one dimension is derived. The Born approximation is then considered in the context of ultracold atoms in a linear harmonic waveguide. In the…
The spectral properties of up to four interacting electrons confined within a quasi one--dimensional system of finite length are determined by numerical diagonalization including the spin degree of freedom. The ground state energy is…
General analytic energy bounds are derived for N-boson systems governed by semirelativistic Hamiltonians of the form H=\sum_{i=1}^N \sqrt(p_i^2+m^2) + \sum_{1=i<j}^N V(r_{ij}), where V(r) is a static attractive pair potential. A…
The nonrelativistic hydrogen atom in $D=3-2\epsilon$ dimensions is the reference system for perturbative schemes used in dimensionally regularized nonrelativistic effective field theories to describe hydrogen-like atoms. Solutions to the…
We present numerical results for the equation of state of an infinite chain of hydrogen atoms. A variety of modern many-body methods are employed, with exhaustive cross-checks and validation. Approaches for reaching the continuous space…
We consider diatomic systems in which the kinetic energy of the electrons is treated in a simple relativistic model. The Born-Oppenheimer approximation is assumed. We investigate questions of stability, deducing bounds on the number $N$ of…
We consider electrostatic interactions in two classes of nanostructures embedded in a three dimensional space: (1) helical nanotubes, and (2) thin films with uniform bending (i.e., constant mean curvature). Starting from the atomic scale…
We analyze the low-lying states for a one-dimensional potential consisting of $N$ identical wells, assuming that the wells are parabolic around the minima. Matching the exact wave functions around the minima and the WKB wave functions in…
Numerical calculations of the electron self-energy without any expansion in the binding nuclear field are required in order to match the rapidly advancing precision of experimental spectroscopy. For the lightest elements, particularly…
The hydrogen phase diagram has a number of unusual features which are generally well reproduced by density functional calculations. Unfortunately, these calculations fail to provide good physical insights into why those features occur. In…
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 problem of computing the thermodynamic properties of a one-dimensional gas of particles which transform in the adjoint representation of the gauge group and interact through non-Abelian electric fields is formulated and solved in the…