Related papers: The relativistic Scott correction for atoms and mo…
We give the asymptotic behavior of the ground state energy of Engel's and Dreizler's relativistic Thomas-Fermi-Weizs\"acker-Dirac functional for heavy atoms for fixed ratio of the atomic number and the velocity of light. Using a variation…
We present a novel technique to obtain relativistic corrections to the central force problem in the Lagrangian formulation, using a generalized potential energy function. We derive a general expression for a generalized potential energy…
After analyzing Dirac's equation, one can suggest that a well-known quantum-mechanical momentum operator is associated with relativistic momentum, rather than with non-relativistic one. Consideration of relativistic energy and momentum…
For rovibronic states corresponding to the $B$ and $B'\ ^1\Sigma_\text{u}^+$ electronic states of the hydrogen molecule, the pre-Born--Oppenheimer (four-particle) non-relativistic energy is converged to a 1-3 parts-per-billion relative…
A model is proposed for the classical electron as a point charge with finite electromagnetic self-energy. Modifications of the Reissner-Nordstr{\o}m (spin 0) and Kerr-Newman (spin 1/2) solutions of the Einstein-Maxwell equations are…
We review some older and more recent results concerning the energy and particle distribution in ground states of heavy Coulomb systems. The reviewed results are asymptotic in nature: they describe properties of many-particle systems in the…
This is the first in a two-part series in which we extend non-relativistic stochastic mechanics, in the ZSM formulation [1, 2], to semiclassical Newtonian gravity (ZSM-Newton) and semiclassical Newtonian electrodynamics (ZSM-Coulomb), under…
We show that the stress-energy tensor has additional terms with respect to the ideal form in states of global thermodynamic equilibrium in flat spacetime with non-vanishing acceleration and vorticity. These corrections are of quantum origin…
We develop a modified semi-classical approach to the approximate solution of Schrodinger's equation for certain nonlinear quantum oscillations problems. At lowest order, the Hamilton-Jacobi equation of the conventional semi-classical…
The phenomenon of quantum vacuum polarization in the presence of a gravitational field is well understood and is expected to have a physical reality, but studies of its back-reaction on the dynamics of spacetime are practically non-existent…
It is argued that by the end of the 1920s a quantum-mechanical model could have been in place, that not only produces the atomic and molecular energy levels of the many-body Pauli equation with Coulomb interactions and external classical…
The energy spectra of atomic ions are re-examined from the point of view of Thomas-Fermi scaling relations. For the first ionization potential, which sets the energy scale for the true discrete spectrum, Thomas-Fermi theory predicts the…
Core-polarization interactions are investigated in low-energy electron elastic scattering from the atoms In,Sn,Eu,Au and At through the calculation of their electron affinities. The complex angular momentum method wherein is embedded the…
We investigate a semiclassical momentum density energy functional for atoms and show that it yields the same value as the well-known Thomas-Fermi functional. In fact, we show an explicit relation between the minimizers of the two…
We review recent progress in the computation of leading quantum corrections to the energies of classical solitons with topological structure, including multi-soliton models in one space dimension and string configurations in three space…
Straight line trajectories are commonly used in semi-classical calculations of the first-order Coulomb excitation cross section at intermediate energies, and simple corrections are often made for the distortion of the trajectories that is…
We present an energy functional for a Thomas-Fermi type two-fluid model of a self-gravitating non-rotating charged body, with a non-relativistic kinetic energy. We prove that, under certain conditions on the total number of positively…
A quantitative test for the validity of the semi-classical approximation in gravity is given. The criterion proposed is that solutions to the semi-classical Einstein equations should be stable to linearized perturbations, in the sense that…
The nonrelativistic Hamiltonians of scalar, spinor and vector particles in the electromagnetic field are studied by applying the Douglas-Kroll-Hess approach. Their relativistic Hamiltonians are expanded on the potential, and the…
We consider a hydrogen-like atom in a quantized electromagnetic field which is modeled by means of the semi-relativistic Pauli-Fierz operator and prove that the infimum of the spectrum of the latter operator is an eigenvalue. In particular,…