Related papers: The relativistic Scott correction for atoms and mo…
By solving the non-relativistic Abraham-Lorentz (AL) equation, I demonstrate that AL equation of motion is not suited for treating the Lorentz atom, because a steady-state solution does not exist. The AL equation serves as a tool, however,…
The nonrelativistic singlet state average $\langle \psi|{\vec a}\cdot\vec \sigma\otimes {\vec b}\cdot\vec \sigma|\psi\rangle =-\vec a\cdot\vec b $ can be relativistically generalized if one defines spin {\it via\/} the relativistic…
This is a brief review of the Thomas-Fermi ("statistical" or "density functional") theory of atoms and molecules.
An analytical expression for the relativistic corrections to the energy spectra of particles completely confined in an one-dimensional limited length in real space is given, based upon the wave property of particles, the relativistic…
The expressions of momentum and energy of a particle in special relativity are often derived in a quite unconvincing manner in elementary text, by resorting either to electrodynamic or quantum considerations, or via the introduction of the…
It is shown that the Foldy-Wouthuysen transformation for relativistic particles in strong external fields provides the possibility of obtaining a meaningful classical limit of the relativistic quantum mechanics. The full agreement between…
We consider the quantum mechanical problem of the motion of a spinless charged relativistic particle with mass$M$, described by the Klein-Fock-Gordon equation with equal scalar $S(\vec{r})$ and vector $V(\vec{r})$ Coulomb plus ring-shaped…
A general approach to analyze the electrodynamics of nuclear matter in bulk is presented using the relativistic Thomas-Fermi equation generalizing to the case of $N \simeq (m_{\rm Planck}/m_n)^3$ nucleons of mass $m_n$ the approach well…
In the first part of this paper, we show that the semiclassical Einstein-Langevin equation, introduced in the framework of a stochastic generalization of semiclassical gravity to describe the back reaction of matter stress-energy…
In solar flares, a large number of charged particles is accelerated to high energies. By which physical processes this is achieved is one of the main open problems in solar physics. It has been suggested that during a flare, regions of the…
We argue that the relativistic correction $\delta{\bf R}_{c.m.}$ to the center-of-mass vector can lead to the approximate equality of the proton and neutron electric polarizabilities in the quark model. The explicit form of $\delta{\bf…
Approximations to the many-fermion free energy density functional that include the Thomas-Fermi (TF) form for the non-interacting part lead to singular densities for singular external potentials (e.g. attractive Coulomb). This limitation of…
Stochastic mechanics (SM), as proposed by Edward Nelson and others in the 20th century, aims to reconstruct quantum mechanics (QM) from a more fundamental theory of classical point particles interacting with a classical-like ether, where…
A relativistic particle in an attractive Coulomb field as well as a static and spherically symmetric gravitational field is studied. The gravitational field is treated perturbatively and the energy levels are obtained for both spin 0…
Extending the work of Park and Strominger, we prove a positive energy theorem for the exactly solvable quantum-corrected 2D dilaton gravity theories. The positive energy functional we construct is shown to be unique (within a reasonably…
We report variational and diffusion Quantum Monte Carlo ground-state energies of the three-dimensional electron gas using a model periodic Coulomb interaction and backflow corrections for N=54, 102, 178, and 226 electrons. We remove…
We present a semiclassical treatment of one-dimensional many-body quantum systems in equilibrium, where quantum corrections to the classical field approximation are systematically included by a renormalization of the classical field…
For molecules and solids containing heavy elements, accurate electronic structure calculations require accounting not only for electronic correlations but also for relativistic effects. In molecules, relativity can lead to severe changes in…
The low-energy amplitude of Compton scattering on the bound state of two charged particles of arbitrary masses, charges and spins is calculated. A case in which the bound state exists due to electromagnetic interaction (QED) is considered.…
We present some basic inequalities between the classical and quantum values of free energy, entropy and mean energy. We investigate the transition from the deterministic case (classical mechanics) to the probabilistic case (quantum…